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NONMELT LASER ANNEALING OF BORON IMPLANTED SILICON 







i 



•> 






By 
SUSAN K. EARLES 






A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 

OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT 

OF THE REQUIREMENTS FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 



UNIVERSITY OF FLORIDA 
2002 



Copyright 2002 

by 
Susan K. Earles 



This work is dedicated to Laurie and her friend, the English major. 



ACKNOWLEDGMENTS 

I would like to thank my research advisor, Dr. Mark E. Law, for his time and support 
beginning in my senior year of undergraduate study and continuing throughout my entire 
course of graduate study. Along with Dr Law, I have also been very fortunate to have 
support throughout the years from Dr Gis Bosman and Dr Robert Fox. Their wonderful 
personalities, character, and advice gave me the courage and desire to continue with my 
graduate study here at the University of Florida. Dr Sheng S Li has also helped me keep 
my sanity by enduring many of my technical questions and thoughts on various topics. 
His advice, support, and encouragement have been very welcome over these last few 
years. I must also thank Dr. Kevin S. Jones. His comments and advice have definitely 
aided in providing direction to my research. Let me also acknowledge Dr Holloway for 
stepping in at the last moment to serve on my committee. It has been a pleasure to have 
the chance to talk with him after class and at various materials science events. I would 
also like to extend a special thanks to Lauren, Edna, Mary, Erlinda, Jim, and Sharon (the 
computer and administrative assistants) for all of their help and conversations over the 
years. 

I would like to thank the groups from Texas Instruments, Lucent, Intel, and Motorola 
for making my intern experiences very enjoyable and sometimes educational. Each 
internship was certainly unique. Mike, Peter, Craig, and Tim definitely made it 
believable that even work can be entertaining. I also want to thank Gana Rimple and 
Somit Talwar at Verdant for help with the laser anneals. Also, although they may be 

iv 



unaware of their positive influence, I am very grateful for and will always welcome 
conversation and advice from Wolfgang Windl and Baylor Triplett. I also need to thank 
the SRC and SEMATECH for the financial support provided for this work. 

As for my friends and family, which I am very fortunate to have, I thank them for all 
of their support. I thank Steve, Janet, Marty, Hernan, Jon, Doug, Lahir, Ibo, Dave, 
Laurie, Michelle, Lesley, Hugo, Joe, Elaine, Heather, Ming-yeh, Meng, Sushil, Wish, 
Aaron, Tony, and the rest of the former and current SWAMP group, for all of the lunch, 
dinner, and phone conversations over the years. It is suddenly obvious why it took me so 
long to finish up. So why stop now, I thank Lisa, Juan, and Derek for all of the much 
needed babble breaks. I would like to let Patrick and my family members, Ester, Lester, 
Beverly, Joe, Beulah, Ron, Angie, Tina, Teresa, Emily, Bob, Gail, Richard, Sandi, Ann, 
Brent, Marissa, and Daniel, "Yes, it is time to buy a stove. I am actually done." 



TABLE OF CONTENTS 

page 

ACKNOWLEDGMENTS iv 

LIST OF FIGURES ix 

ABSTRACT xv 

1 INTRODUCTION 1 

1.1 Motivation and Objective 1 

1.2 Ion Implantation 2 

1.2.1 Collisions and Damage 3 

1.2.2 Complications 4 

1.3 Activation 5 

1.4 Annealing and Diffusion 6 

1.4.1 Overview 6 

1.4.2 Rapid Thermal Annealing 8 

1.4.3 Laser Annealing 9 

1.5 Analysis Techniques 1 1 

1.5.1 Chemical 11 

1.5.2 Electrical 11 

1.5.3 Structural 13 

2 LASER ANNEALING 20 

2.1 Overview 20 

2.2 Laser Beam Interaction with Silicon 20 

2.3 The Temperature Model 21 

2.4 Laser Interaction with Implanted Silicon 23 

2.4.1 Absorption Depth and Implant Energy 24 

2.4.2 Silicon Interstitial and Boron Diffusion during Annealing 24 

2.4.3 Increasing the Number of Laser Pulses 26 

2.5 Determining the Melting Point 27 

2.5.1 The 308 nm Melting Point 27 

2.5.2 The 532 nm Melting Point 28 



3 EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON 
IMPLANTED SILICON: 308 NM EXCIMER LASER 38 



VI 



3.1 Overview 38 

3.2 Experiments 39 

3.2.1 Increasing the Number of Laser Pulses: 308 nm Laser, 5 KeV Boron Implant 
39 

3.2.2 Increasing the Number of Pulses: 308 nm Laser, 1 KeV Boron Implant 39 

3.3 5 KeV Results and Discussion 39 

3.4 1 KeV Results and Discussion 41 

3.5 Concluding Remarks 43 



4 EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON 
IMPLANTED SILICON: 532 NM RUBY:YAG LASER 50 

4.1 Introduction 50 

4.2 Increasing the Number of Pulses: 532 nm Laser, 500 eV Boron Implant 50 

4.2.1 Experiment 50 

4.2.2 Results and Discussion 51 

4.3 Increasing the Number of Pulses: 532 nm Laser, 5 KeV Boron Implant 52 

4.3.1 Experiment 52 

4.3.2 Results and Discussion 52 



5 EFFECTS OF POST-PROCESSING AFTER NONMELT LASER ANNEALING .... 61 

5.1 Overview.™ 61 

5.2 High-Temperature Rapid Thermal Annealing after 308 nm NLA 61 

5.2.1 Experimental Overview 61 

5.2.2 5 KeV Results 62 

5.2.3 1 KeV Results 64 

5.2.4 Discussion 65 

5.3 High-temperature rapid thermal anneals after 532nmNLA 66 

5.3.1 Experimental Overview 66 

5.3.2 5 KeVResults and Discussion 67 

5.3.3 500 eV Results and Discussion 68 

5.4 Furnace Anneals and Damage Evolution 71 

5.4.1 308nm NLA 71 

5.4.2 532nm NLA 72 

5.5 Conclusions 72 



6 EFFECTS OF NLA ON MOBILITY AND ACTIVATION 89 

6.1 Introduction 89 

6.2 Experimental Results 90 

6.2.1 The 308 nm Experiments 90 

6.2.2 The 532 nm Experiments 91 

6.3 Discussion 92 



vn 



6.3.1 Overview 92 

6.3.2 Boron Activation, Deactivation, and Precipitation 93 

6.3.3 Boron Activation, Deactivation, Interstitial s, and Diffusion 96 

6.3.4 Mobility and Sheet Resistance 97 

6.3.5 Mobility, Activation, and Loops 98 

6.4 Conclusions 100 



7 MODELING THE MOBILITY 1 17 

7.1 Introduction 117 

7.2 Li's and Linares' Mobility Model 118 

7.3 The Improved Mobility Model 1 19 

7.4 Conclusions 122 



8 SUMMARY, CONCLUSIONS, AND FUTURE WORK 130 

8.1 Summary 130 

8.2 Conclusions 132 

8.3 Suggestions for Future Work 133 



APPENDIX 

A TEMPERATURE SIMULATION DURING NLA USING FLOOPS 135 

B MODELING THE MOBILITY WITH FLOOPS 153 

LIST OF REFERENCES 158 

BIOGRAPHICAL SKETCH 162 



vui 



LIST OF FIGURES 
Figure page 

1.1 Schematic of MOS transistor showing location of source drain extensions (SDE) 15 

1.2 Top plot shows the average diffusion length of a silicon interstitial after 1 ns and 10 

ns. The bottom plot shows the diffusion lengths for boron after 1 ns and 10 ns for 
intrinsic and transient enhanced (B-I Pair diffusion) diffusion 16 

1.3 The diffusion length of the silicon is divided by the diffusion length of the boron 

interstitial pair and plotted versus temperature. This shows how much farther a 
silicon interstitial can travel than a boron-interstitial pair at the same time and 
temperature 17 

1 .4 This plot shows how fast the surface cools after reaching a peak temperature of 

1600K (1327°C). The top plot shows how long it takes to cool to room 
temperature. The bottom plot shows how long it takes to cool to around 800°C. ... 18 

2.1 This plot shows the temperature versus time seen at various depths in the wafer 

during the NLA. The top curve is the temperature at the surface of the wafer. The 
bottom curve is the temperature at 100 A into the wafer 29 

2.2 This figure shows the temperature distribution in the wafer during one 20ns pulse 

with the 532 nm laser. It also shows the beginning of the cool down after the 
pulse is turned off (time > 2.0xl0" 8 s) 30 

2.3 This plot shows the temperature versus time seen at the surface of the wafer when 

the sample is irradiated with multiple pulses at a frequency of 100Hz 31 

2.4 These plots are magnified views of the plot in Figure 2.3. This shows a more 

detailed view of how the temperature is distributed over depth during the 532nm 
NLA 32 

2.5 Illustration of the approximate amount of the 5 KeV boron implant which is 

annealed during a 308 nm NLA. The entire area is annealed during a 532 nm 
NLA 33 

2.6 Sheet resistance vs laser energy density in 5 KeV, lel5 B+/cm2 samples irradiated 

with one 15 ns pulse using the 308 nm laser 34 



IX 



2.7 Reflectivity versus laser energy density after one pulse with the 308 nm laser on 5 

KeV, 2el5B+/cm2 samples 35 

2.8 Sheet resistance versus laser energy density for the 5 KeV, 2el5 B+/cm2 samples 

following one 20 ns pulse with the 532 nm laser 36 

2.9 Reflectivity versus laser energy density for 5 KeV, 2el5 B+/cm 2 samples annealed 

with the 532 nm laser using a 20 ns pulse 37 

3.1 SIMS of 5 KeV, 2el5 B+/cm2 samples as-implanted and after the NLA with 308 nm 

laser, and after 1040°C,5 sec RTA 44 

3.2 Sheet resistance number of laser pulses for 5 KeV, 2el5 B+/cm2 samples following 

an NLA with the 308 nm laser at 0.6 J/cm2. using a pulselength 15 ns and a 
frequency of 10 Hz 45 

3.3 Plan-view TEM for 5 KeV, 2el5 B+/cm 2 samples following one pulse (top left), 10 

pulses (top right), 100 pulses (bottom right), and after a 1040°C, 5 sec RTA 
(bottom right). For the NLA the 308 nm laser is used with a 15 ns pulse at a 
frequency of 10 Hz and a laser energy density at 0.6 J/cm 2 46 

3.4 SIMS of the 1 KeV, lel5 B+/cm2 samples as-implanted, after ten pulses, and after a 

1040oC, 5 sec RTA. The 308 nm laser with a 15 ns pulse at 10 Hz is used 47 

3.5 Sheet resistance versus number of laser pulses for the 1 KeV, lei 5 B+/cm2 samples 

using the 308 nm laser with a 15 ns pulse at 10Hz. The point at pulses 
represents the sample that just received the 1040°C, 5 sec RTA 48 

3.6 Plan-view TEM of the 1 KeV, lel5 B+/cm2 samples after 10 pulses using the 308 

nm laser with a 1 5 ns pulse at 1 0Hz (left) and after the 1040°C, 5 sec RTA(right).. 49 

4.1 SIMS of the boron profiles as-implanted, following the NLA, and following the 

1050°C spike anneal for the 500 eV, lel5 B+/cm 2 samples 54 

4.2 Sheet resistance versus number of laser pulses for 500 eV, lei 5 B+/cm 2 samples 

annealed with the 532 nm laser at 0.35 J/cm 2 using a 20 ns pulse 55 

4.3 Plan-view TEM of the 500 eV, lei 5 B+/cm 2 samples annealed with a 1050C spike 

anneal 56 

4.4 SIMS of the boron profiles as-implanted, following the NLA, and following the 

spike anneal for the 5 KeV, 2el5 B+/cm 2 samples 57 

4.5 Plan-view TEM of the 5 KeV, 2el5 B+/cm 2 samples annealed with the 532 nm laser 

at 0.35 J/cm 2 using one, 10, 100, and 1000 pulses at 100Hz and 20 ns/pulse 58 

4.6 Sheet resistance versus number of laser pulses for 5 KeV, 2el5 B+/cm 2 samples 

annealed with the 532 nm laser at 0.35 J/cm 2 using a 20 ns pulse 59 



4.7 Sheet resistance versus junction depth comparing NLA and the conventional spike 

anneal for a 500 eV and a 5 KeV boron implant 60 

5.1 SIMS profiles following NLA and 1000°C, 5sec RTA for 5 KeV are shown, lei 5 

B+ ions/cm 2 samples processed with the 308 nm laser 73 

5.2 Sheet Resistance vs. Laser Energy Density following 1000°C, 5sec RTA for 5 

KeV. Iel5 B+ ions/cm 2 samples processed with the 308 nm laser 74 

5.3 TEM following 0.4 J/cm 2 NLA following 0.6 J/cm 2 NLA, and following the RTA 

(top pictures from left to right), and TEM of samples receiving 0.4, 0.5, or 0.6 

J/cm NLA followed by RTA (bottom pictures from left to right) 75 

5.4 Percentage of loops extending to the surface versus laser energy density for 

1000°C, 5sec RTA of 5 KeV. Iel5 B+ ions/cm 2 samples processed with the 308 
nm laser 76 

5.5 Defect density versus laser energy density for 1000°C, 5sec RTA of 5 KeV. lei 5 

B+ ions/cm 2 samples processed with the 308 nm laser 77 

5.6 SIMS of 1 KeV, 10 15 ions/cm2 B following 10 laser pulses, with 1040°C, 5 sec 

RTA, and 10 pulse plus 1040°C, 5 secRTA 78 

5.7 Sheet resistance versus number of laser pulses for 1 KeV, 10 15 /cm2 B for samples 

receiving just the NLA (NLA only) and those processed with 1040°C, 5 sec RTA 
(with RTA) 79 

5.8 Plan-view TEM of 1 KeV, lel5/cm 2 boron implanted silicon following (from left 

to right) 10 shots, RTA only, 10 shots plus RTA 80 

5.9 SIMS of 5 KeV, 2el5 B+ ions/cm 2 samples following NLA with the 532 nm laser 

using a 20 ns pulse length at 100 Hz and 1050°C spike anneal compared with the 
sample receiving just the spike anneal 81 

5.10 Sheet resistance versus number of laser pulses of 5 KeV, 2el5 B+ ions/cm 2 

samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 
Hz and/or 1050°C spike anneal 82 

5.11 Plan-view TEM of 5 KeV, 2el5 B+ ions/cm 2 samples following RTA alone, one 

pulse plus RTA, and 10 pulses plus RTA. The NLA is at 0.35 J/cm 2 with the 532 

nm laser using a 20 ns pulse length at 100 Hz. The RTA is a 1050°C spike 

anneal 83 

5.12 SIMS of 500 eV, lel5 B+ ions/cm 2 samples following NLA with the 532 nm laser 

using a 20 ns pulse length at 100 Hz and 1050°C spike anneal compared with the 
sample receiving just the spike anneal 84 



XI 



5.13 Sheet resistance versus number of laser pulses of 500 eV, lel5 B+ ions/cm 2 

samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 
Hz and/or 1050°C spike anneal 85 

5.14 Plan-view TEM of the 500 eV, lel5 B+/cm 2 sample annealed with a 1050°C spike 

anneal 86 

5.15 Plan- view TEM of 5 KeV, lei 5 B+ ions/cm 2 samples after 750°C furnace anneal 

(top left), NLA plus 750°C, 15 min furnace anneal (top right), NLA plus 750°C, 
45 min furnace anneal (bottom left), and NLA plus 750°C, 90 min furnace anneal 
(bottom right). The NLA is with the 308 nm laser using one 15 ns pulse at 0.6 
J/cm 2 87 

5.16 Sheet resistance for the 5 KeV, 2el5/cm 2 samples receiving the 532 nm NLA 

and/or the 750°C furnace anneal 88 

6.1 The Hall mobility vs. laser energy density is shown following 1040°C, 5 sec RTA 

for 5 KeV, 2el5 B+ ions/cm 2 samples processed with the 308 nm laser 102 

6.2 Plot of the percent activation vs. laser energy density following 1040°C, 5 sec RTA 

for 5 KeV, 2el5 B+ ions/cm 2 samples processed with the 308 nm laser. The 
active dose measured with Hall effect is divided by the implanted dose of 2el5 
ions/cm 2 which is also the dose measured from SIMS 103 

6.3 Mobility and active dose (hole density) versus number of laser pulses for 1 KeV, 

10 15 /cm2 B for samples receiving just the NLA (NLA only) and those processed 
with 1040°C, 5 sec RTA (with RTA) 104 

6.4 Percent activation versus number of laser pulses for 1 KeV, 10 15 /cm2 B for 

samples receiving just the NLA (NLA only) and those processed with 1040°C, 5 
sec RTA (with RTA). Top picture represents the active dose divided by the dose 
of the implant, lei 5 ions/cm 2 and the bottom picture the active dose divided by 
the dose determined from SIMS, 7.4el5 ions/cm 2 105 

6.5 Mobility and hole density versus number of laser pulses of 5 KeV, 2el5 B+ 

ions/cm 2 samples following NLA with the 532 nm laser using a 20 ns pulse length 
at 100 Hz and/or 1050°C spike anneal 106 

6.6 Percent activation versus number of laser pulses of 5 KeV, 2el5 B+ ions/cm 2 

samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 
Hz and/or 1050°C spike anneal. The active dose is divided by the dose of the 
implant, lel5 ions/cm 2 107 

6.7 Mobility and hole density versus number of laser pulses of 500 eV, lei 5 B+ 

ions/cm 2 samples following NLA with the 532 nm laser using a 20 ns pulse length 
at 100 Hz and/or 1050°C spike anneal 108 



Ml 



6.8 Percent activation versus number of laser pulses of 500 eV, 1 e 1 5 B+ ions/cm 2 

samples following NLA with the 532 ran laser using a 20 ns pulse length at 100 
Hz and/or 1050°C spike anneal. The top picture is for the active dose divided by 
the dose of the implant, lei 5 ions/cm 2 , and the bottom picture is for the active 
dose divided by the actual SIMS dose 109 

6.9 Dose loss as a result of processing with the NLA and/or the RTA in the 500eV 

samples processed with the 532 nm laser. The top plot shows the dose measure 

from SIMS following each anneal step. The bottom plot shows the percent of 

dose which is lost during the RTA 1 \q 

6.10 Hole density and hole mobility versus sheet resistance measured using Hall effect. 

As shown, the change in sheet resistance is not dominated by change s in 

mobility, but by the hole density m 

6.1 1 Hole mobility versus loop density and interstitial density are plotted. No strong 

trends exist over all of the data 1 12 

6.12 Percent activation versus loop density and interstitial density 113 

6.13 Hole mobility versus hole concentration for all processing conditions. The hole 

concentration is determined by dividing the hole density by the junction depth 
measured at a boron concentration of lxl0 18 /cm 3 1 14 

6.14 Sheet resistance as a function of junction depth for all processes (top) and NLA 

alone compared with the conventional RTA (bottom). Xj is measured at a boron 
concentration of lxl0 18 /cm 3 . The arrows show the benefit of using NLA over 
conventional processing anneals 1 15 

6.15 Plots of the hole density and hole mobility are shown versus the average radius of 

the loops. As you can see both plots show strong trends. As the average radius of 
the loops increases, the hole density decreases and the hole mobility increases 1 16 

7. 1 This plot compares the theoretical results to the experimental results for the hole 

mobility versus number of laser pulses after 532 nm NLA. The 5 KeV, 2el5/cm2 
samples are used 224 

7.2 This plot compares the theoretical results with the experimental results for the hole 

mobility versus number of laser pulses. The 1 KeV, Iel5/cm2 sample results 
shown here are processed with the 308 nm laser 125 

7.3 The hole mobility versus the number of laser pulses is shown for the 5 KeV, 

2el5/cm2 samples processed with the 532nm laser. The simulation used here 
included the dependence of the number of neutrals on the size of the loop 126 

7.4 The sheet resistance versus the number of laser pulses is shown for the 5 KeV, 

2el5/cm2 samples processed with the 532nm laser. The simulation used here 
included the dependence of the number of neutrals on the size of the loop 127 



Xlll 



7.5 The mobility versus the number of laser pulses is shown for the 1 KeV, Iel5/cm2 

samples processed with the 308nm laser. The simulation used here included the 
dependence of the number of neutrals on the size of the loop 128 

7.6 The sheet resistance versus the number of laser pulses is shown for the 1 KeV, 

Iel5/cm2 samples processed with the 308nm laser. The simulation used here 
included the dependence of the number of neutrals on the size of the loop 129 



xiv 



Abstract of Dissertation Presented to the Graduate School 

of the University of Florida in Partial Fulfillment of the 

Requirements for the Degree of Doctor of Philosophy 

NONMELT LASER ANNEALING OF BORON IMPLANTED SILICON 

By 

Susan K. Earles 

May 2002 

Chair: Mark E. Law 

Department: Electrical and Computer Engineering 

A new method for creating heavily-doped, ultra-shallow junctions in boron-implanted 

silicon will be presented. This method uses nonmelt laser annealing (NLA) to supply 

energy to the surface region of the silicon at a ramp rate greater than 10 10o C/sec. This 

study concentrates on high-dose, non-amorphizing boron implants. Boron implants into 

silicon at energies of 500 eV to 5 KeV at doses of lei 5 - 2e 15 ions/cm2 are used. 

Samples are analyzed using the following techniques: four-point probe (FPP), Hall 

effect, secondary ion mass spectroscopy (SIMS), and transmission electron microscopy 

(TEM). The results from FPP and SIMS show increasing the number of laser shots 

decreases the sheet resistance without increasing the junction depth. Hall effect 

measurements show NLA can also increase the mobility. Also, NLA affects defect 

nucleation. Following NLA numerous small defects are nucleated resulting in a dramatic 

change in the defect population. This decrease in defect size and increase in population 

are shown to increase the scattering in the layer which decreases the mobility. Using 



xv 



NLA, heavily-doped 20 nm p-type layers with sheet resistances around 600 Ohms/sq are 
created. Also, NLA results in nearly 100% activation of the boron in the sample and 
reduces the dose loss during post-processing. 

To help understand the changes in defect populations and mobility measurements 
introduced by the NLA, experiments as well as modeling efforts are made. A mobility 
model implemented in FLOOPS (Florida's Object Oriented Process Simulator) with 
terms to account for these defects is presented. With this mobility model the sheet 
resistance of the implanted layer as well as the mobility can be determined. Also, the 
temperature distribution in the silicon during the NLA and the cool-down will be 
implemented in FLOOPS. This temperature distribution along with the current process 
simulation models allows the calculation of the defect population following the NLA to 
be determined, thus allowing more accurate modeling during post anneals. 



xvi 



CHAPTER 1 
INTRODUCTION 

1 . 1 Motivation and Objective 

Industry and individual consumer demand will always require electronic equipment to 
offer more functions and ease of use while costing less, operating faster, and occupying 
less space. When that electronic equipment contains integrated circuits (ICs), these 
demands can often be met by shrinking the ICs. However, reducing the size of integrated 
circuits relies on the ability to shrink feature sizes at all levels from the metal 
interconnect lines down to the individual transistors. In the semiconductor industry, the 
most common way to make these individual transistors is using the complementary 
metal-oxide-semiconductor (CMOS) process using silicon [Jae93]. 

The CMOS transistors are considered n-type (NMOS) or p-type (PMOS) depending 
on which carrier (electrons or holes) forms the channel in the device. One of the key 
issues involved in scaling PMOS transistors is reducing the depth of the p-type 
source/drain extensions (Figure 1.1). For example, junction depths less than 30 nm are 
required for 70 nm gate lengths [Cur97]. The simplest method of producing p-type 
junctions is to implant boron, a p-type dopant. After the implant, the wafer is typically 
rapid thermally annealed (RTA) in an effort to activate the boron and remove damage 
created by the implant. Ideally during the RTA the following events would occur: the 
boron would stay in the region where it was implanted, each of the boron atoms would 
occupy a substitutional site in the lattice resulting in 100% activation of the implanted 
dopant, and the damage to the lattice created during the implant would be completely 

1 



removed. However upon annealing, the heating of the lattice and the damage from the 
implant result in boron diffusion, boron clustering, and defect evolution [Cow90, Hof74, 
Sol90]. This produces deeper junctions, lower boron activation, and reduced mobility. 
Variations in the implant parameters and thermal annealing techniques are thus required 
to produce shallower junctions. 

Experiments show increasing the ramp-up rate during thermal processing has been 
shown to decrease the transient enhanced diffusion (TED) of boron in silicon [Aga98, 
Aga99, Dow99]. Plots of the ramp-up rate versus diffusion length show the ramp-up rate 
would need to be around 10 10 °C /sec to result in a diffusion length of zero, and hence no 
TED [Cow96]. Unfortunately, conventional RTA systems have peak ramp-up rates of 
200-400 °C. However, using a laser for thermal processing results in a ramp-up rate 
which approaches the 10 10 °C /sec that current data suggests is needed for zero TED. The 
ramp-down or cooling rate is also dramatically higher for the laser-annealed sample since 
only a small surface region of the wafer is heated during the nonmelt laser anneal (NLA). 
Therefore, in an effort to reduce TED while achieving high dopant activation, the 
following study investigates the effects of nonmelt laser annealing on silicon heavily- 
doped with boron. 

1.2 Ion Implantation 
Silicon requires the addition of impurities to improve its conductivity. When 
impurities are intentionally added to silicon they are called dopants. Ion implantation is 
the most practical technique available for introducing dopants into silicon. Ion 
implantation is a process which is controllable and reproducible. Other methods which 
introduce dopants via solid-source or gas diffusion are difficult to control and not as 
reliable. These methods are also limited in the ability to only incorporate dopants up to 



the solid solubility level. Ion implantation, however, allows dopants to be introduced into 
the silicon at values above solid solubility. 
1.2.1 Collisions and Damage 

Essentially, during ion implantation a source of the desired dopant is vaporized and 
then ionized. The ionized atoms can then be sorted via a mass analyzer. The desired 
species can then be filtered out, producing a source of high purity ions for implantation. 
Under a strong electric field, the desired ions can then be directed and accelerated into a 
beam which can be aimed at the target which is the surface of the silicon wafer. 

While the dopant atoms are being directed to the silicon surface, collisions between 
atoms and electrons will occur, energy will be exchanged, and many dopant atoms will 
lose energy and come to rest below the surface of the silicon. The ion can lose energy via 
a combination of two processes: nuclear stopping or electronic stopping. For nuclear 
stopping, the elastic scattering between the ion and nuclei of the solid is considered. 
Electronic stopping is quite complicated. The inelastic scattering events must also be 
considered since the ion interacts with the electrons in the crystal. This interaction can 
cause ionization of the target (silicon) atoms, ionization of the implanted ion, and 
excitation of valance and conduction band electrons. 

These two stopping methods are used in calculations along with the implant energy to 
determine the total distance the dopant ion travels into the silicon. The energy and angle 
at which the dopant ions hit the surface determines how far the dopants reside below the 
surface. The beam current and implant time determines how many dopant atoms will be 
incorporated into the silicon. Typically the process designer is concerned with the 
projected range, which is the average depth the dopant penetrates below the surface and 
the projected straggle, which is the deviation from the projected depth. More detail on 



the implantation process can be found in numerous books [W0I86, Sze88, Smi77], 
dissertations [BriOl, LilOl, Liu96], and theses [Mil99, Liu94]. 

When the dopant collides with the silicon lattice, silicon atoms are often displaced, 
increasing the number of silicon interstitials in the silicon lattice. Approximately 15 eV 
is required to displace a silicon atom from its lattice site [Sze88]. Displaced atoms with 
sufficient energy can then collide with other atoms causing them to be displaced. This 
new interstitial profile is typically referred to as the damage profile. Aside from the dose 
and energy of the implanted species, the damage profile is also affected by the mass of 
the implanted species, the temperature of the silicon during implant, and the rate at which 
the ions hit the silicon. For example, heavier, larger atoms and molecules such as 
arsenic or BF2 implanted at a dose of lei 5 ion/cm 2 and an energy of 5 KeV will create 
more damage than boron atoms implanted at the same dose and energy. If the damage is 
great enough, the silicon can be converted from crystalline to amorphous, which means it 
lacks long-range order. 

The amount of damage created will determine which type of defect evolves when the 
wafer is heated. Jones et al. [Jon88] created a classification system for defects based on 
the damage profiles from which they evolved. Type I extended defects form below 
amorphization while Type II - IV require amorphization. Type V defects are considered 
to occur when the implant dose approaches the solid solubility limit of the dopant in 
silicon. Type V are generally considered to result in precipitates upon annealing. 
1 .2.2 Complications 

Typically (100) silicon wafers are used in processing. For this surface, implanting 
boron at an angle of zero degrees results in the most channeling. Often boron is 
implanted at 7 degrees to minimize the channeling. However, there is much debate as to 



whether implanting at an angle has any benefit for ultrashallow boron implantation. As 
the implant energy is reduced the implantation process itself becomes more complex. 
Lower implant energies are required to produce the shallower junctions. However, the 
dopant must still have enough energy to penetrate the silicon. This limits the minimum 
energy at which boron can be implanted. Also, during implantation surface sputtering 
occurs. For deep profiles the majority of atoms sputtered off the surface are silicon 
atoms. As the projected range of the dopant moves towards the surface and the surface 
concentration of dopant increases, the atoms sputtered begin to become a mix of silicon 
and the dopant. This results in a loss of dopants (dose-loss) and makes it more difficult to 
predict the characteristics of the implanted layer 

If the dose is high enough for a particular energy, the surface can become amorphized. 
Amorphizing the surface prior to a laser anneal will cause complications as the 
amorphized region will melt at a temperature around 200°C lower than crystalline silicon. 
Also, when a region has become amorphized the effects of end-of-range (EOR) damage 
developing during post-annealing must also be considered. For more information on ion- 
implantation the reader is encouraged to view Andreas Hossinger's dissertation, 
Simulation of Ion Implantation for ULSI Technology, at www.iue.tuwien.ac.at [HosOO]. 

1.3 Activation 
During the post implantation anneal energy must be applied to the implanted region to 
activate the boron. Activation typically involves substituting a boron atom for a silicon 
atom in a lattice site. Silicon crystallizes in the diamond lattice structure, which has a 
coordination number of 4. This means each of the silicon atoms is bonded to four 
neighboring silicon atoms. When a p-type dopant (B, In, Al, or Ga) with three valence 
electrons replaces one of the silicon atoms, it accepts another electron from crystal to 



complete all four bonds. This produces a negatively charged ion and effectively results 
in the donation of a hole to the valence band. This hole is now available to participate in 
conduction. N-type dopants (P, As, and Sb), having five electrons available for bonding, 
will similarly donate an electron to the conduction band when replacing a silicon atom. 
Once substitutional, the energy needed to ionize the dopant being small (~a few 
hundredth eVs) is easily supplied by lattice vibrations occurring at room temperature. 
However, the energy needed to move the boron into a substitutional site (a few eVs) 
typically requires an anneal step far above room temperature. 

1.4 Annealing and Diffusion 
1.4.1 Overview 

Dopant activation, defect evolution, and dopant-defect interactions are all driven by 
diffusion processes that occur during annealing. It is generally accepted that dopants 
diffuse in silicon by interactions with interstitials, vacancies, or both. Boron is 
considered to be a purely interstitial diffuser meaning it needs an interstitial to diffuse. 
Many models have been created to predict the diffusion of various dopants in silicon 
[LilOl, Gen99]. Many studies [Fai90, Cha96, Cow96, Sto97] have been performed to 
show that during annealing, dopants, in the presence of damage such as excess 
interstitials or vacancies, diffuse at rates which differ from the predicted equilibrium 
values. For example, numerous studies show that boron in the presence of a high 
concentration of interstitials will show increased diffusion or transient-enhanced 
diffusion (TED) [Sto97, Pri99, Nap99, NapOO]. It is also believed that at high doses, 
boron, in the presence of a high concentration of interstitials forms into immobile, 
inactive or partially ionized clusters, or boron interstitial clusters (BICs) [Sto97, Col98a, 
Col98b, ColOO, LilO 1 ]. Also, extended defects which evolve during the anneals are 



believed to getter boron making it inactive. Increased diffusion and dopant deactivation 
are both detrimental to obtaining an ultrashallow, highly doped layer. Thus, removal of 
the excess interstitial population is essential. 

The amount of damage removal and boron diffusion is determined by how much the 
silicon interstitial and boron diffuse during the anneal step. The peak temperature and 
time at peak temperature along with how fast the wafer is heated and cooled all add to the 
thermal budget seen by the wafer. The diffusion length is calculated as 

L = (Dt) 1/2 (1.1) 

where D is the diffusivity in cm 2 /s, and t is the time in seconds. The diffusivities used 
were calculated using the expression: 

D = Do exp(E a /kT) (1.2) 

where D is the exponential prefactor, E a is the activation energy, k the Boltzmann's 
constant, and T the temperature. Using diffusivities generated by Florida's Object 
Oriented Process Simulator (FLOOPS), Figure 1.2 shows how the diffusion length of 
silicon compares to that of boron over many different temperatures. The top plot shows 
the diffusion length of the silicon interstitial after 1 ns and 10 ns at temperatures ranging 
from 1200-1400°C. The bottom plot shows how far a boron atom can move in silicon 
after 1 ns or 10 ns. The plot shows the intrinsic diffusion as well as the enhanced 
diffusion which occurs when the boron pairs with an interstitial to diffuse. From these 
figures it is shown that silicon diffuses remarkably faster than boron with the gap 
between the diffusion lengths at a set time narrowing as the temperature is increased. To 
further illustrate how much faster the silicon interstitial diffuses compared to the boron 
interstitial pair, Figure 1.3 is presented. In this figure the diffusion length of the silicon 



g 

interstitial after 1 ns is divided by the diffusion length of the boron interstitial pair after 1 
ns. At 1300°C, the silicon interstitial diffuses on average 1000 times farther than the 
boron-interstitial pair. 
1.4.2 Rapid Thermal Annealing 

Rapid thermal annealing (RTA), also referred to as rapid thermal processing (RTP), is 
the most popular technique used today to activate dopants following ion implantation. 
The systems available process one wafer at a time. The system configurations can vary 
greatly. However, for shallow junction formation, the goal is the same: rapidly heat the 
wafer to a high temperature (900-1 100°C) for a short time (a few seconds or less). 
Lower temperatures for such short times result in little to no dopant activation and 
insufficient damage removal. The time the wafer is held at peak temperature is often 
referred to as the soak time. Ramp-up rates of 40-400°C are available [Aga99]. A 
popular type of RTA is a spike anneal. This involves ramping the wafer up to peak 
temperature and then ramping it down, holding it for only a few milliseconds at peak 
temperature. The ramp-up rate and minimum hold time at peak temperature is limited by 
the system configuration. Two common configurations are the lamp-based system and 
the hot-walled system. 

Since the process involves heating the whole wafer, the wafer is ramped up to 600- 
700°C where it is held for a few seconds before ramping up to peak temperature. This 
reduces the effects of stress that develops in the wafer due to thermal gradients and layers 
with mismatched lattice constants. Unfortunately, the hold at 600-700°C increases the 
thermal budget of the process. Also, since the whole wafer is heated, the whole wafer 
has to cool down. The wafer cools by radiative cooling from the wafer surfaces and 
conduction through the wafer holder. The lamp-based system has been shown to cool at 



~70°C/sec and the hot-walled system at ~60°C/sec [Aga99, Aga98]. The slow cool-down 
rates also add to the thermal budget seen by the wafer. 
1 .4.3 Laser Annealing 

As previously mentioned, increasing the ramp-rate during RTA results in decreased 
dopant diffusion [Aga99, Aga98, Dow99]. However, even the fastest available RTA 
systems peak at a few hundred degrees Celsius per second. This prompts the need for an 
anneal system with a faster ramp-rate. Laser annealing provides the fast ramping desired. 
Laser annealing also offers faster cooling rates and reduces the thermal budget seen by 
the wafer. 

Laser annealing has also been referred to as laser thermal annealing (LTA) and laser 
thermal processing (LTP). Many different types of lasers have been used. The YAG, 
excimer, and C02 lasers are some of the more common ones. Studies of the effects of 
laser radiation on solids date back to 1971 [Rea71]. Excimer laser annealing (ELA), for 
example, uses an excited-dimer (excimer) laser for annealing. 

During laser annealing a beam of photons is focused on a sample. Simply put, the 
photons interact with the electrons in the sample which then transfer the energy to the 
lattice. This causes localized heating in the area where the photons hit the sample. More 
specifically, the wavelength of this light determines how the energy will be absorbed in 
the silicon. The energy of the beam, or incident photon energy, is determined by the 
equation: 

E=hc/X (1.3) 

with h equal to Planck's constant, c equal to the speed of light, and X equal to the 
wavelength of the laser. With the bandgap of silicon around 1 . 1 2 e V laser energy greater 



10 

than this bandgap results in absorption via band-to-band transitions, which results in the 
desired heating of the region. Since only a specific region of the material is heated the 
wafer cools via surface radiation and thermal conduction. The high thermal conductivity 
of silicon allows the region to cool from 1600K (1326°C) to room temperature in a few 
tenths of a millisecond. This cooling rate can be calculated from Figure 1.4. 

Previous studies have investigated the use of high power pulsed lasers to melt the 
implanted layers to achieve high activation and abrupt junctions [Tsu99, Zha95]. 
Complications arising from melting and regrowth, however, limit the use of this 
technique [ChoOO, PriOO, Tsu99, Zha95]. When a region of the silicon is melted, a melt 
front develops which increases the heated volume. Melted regions also recrystallize off 
of the region which is not melted. Recrystallization off of an oxide, for example, would 
result in polycrystalline material. To avoid the negative effects of melting the wafer, the 
power of the laser can be reduced to produce heating without melting. This will be called 
nonmelt laser annealing (NLA). 

A typical sequence for the front end processing which leads up to the ultrashallow 
junction anneal would be as follows: 

1. Active area formation 

2. N-well implant plus channel doping 

3. Gate oxidation 

4. Gate electrode fabrication 

5. Gate reoxidation 

6. Pre-amorphization implant 

7. Dummy side-wall spacer formation 

8. Source-drain implant 

9. Side-wall spacer removal plus RTA 

10. Extension implantation (ultrashallow layer) 

1 1 . Ultrashallow junction anneal (RTA or possibly a laser anneal) 



11 

Previous studies have investigated the use of high power pulsed lasers to melt the 
implanted layers to achieve high activation and abrupt junctions [Tsu96, Tsu99, Zha95]. 
Complications arising from melting and regrowth, however, limit the use of this 
technique [ChoOO, PriOO, Zha95]. 

1.5 Analysis Techniq ues 
1.5.1 Chemical 

Secondary ion mass spectroscopy (SMS) is a destructive technique which can be used 
to obtain a concentration versus depth profile of impurities in silicon. Typically, the 
impurity of interest is the implanted dopant, which for this study is boron. During SIMS 
a beam of ions is directed at the surface of the sample. When the beam hits the surface, it 
causes atoms and molecules to be ejected, resulting in sputtering of the surface. These 
ejected species are generally charged and hence termed secondary ions. These secondary 
ions are then sent through a mass analyzer. A profile of the number of each species 
detected at a particular mass is then obtained over the depth of sputtering. From this 
profile the concentration versus depth profile of the impurity of interest is obtained. 

As the implant energies are reduced and the layers more heavily doped the limitations 
of SIMS begin to become apparent. Various debates exist over what part of the SIMS 
profiles are real. Long tails in the profiles, which have been attributed to rough crater 
bottoms, make it difficult to accurately determine junction depths and effective 
diffusivities. 
1.5.2 Electrical 

To understand how the created layer can be used in a device, the electrical properties 
of that layer must be known. The electrical properties are defined by the resistivity, the 
carrier density, and the carrier mobility. The resistivity of the layer is dependent upon the 



12 

number of carriers present and the mobility of those carriers in that layer. For a single 

type of carrier with a positive charge (a hole) resistivity is defined as 

P = 1/qnn (1.4) 

where p is the resistivity, q is the charge of the carrier (1.602x1 19 C), fi is the carrier 

mobility, and n is the density of free charges, or carrier density. 

The four-point probe (FPP) is commonly used to measure the resistance of a layer. 
The sheet resistance along with the thickness of the layer gives the resistivity. The four- 
point probe applies a current between two points to the surface and measures the resulting 
voltage between the other two points. The tips of the probe are made of a very strong, 
low resistivity metal and applied to the surface of the wafer with enough pressure to 
effectively punch through any native surface oxide. To obtain the correct sheet 
resistance, a correction factor based on the spacing of the probe tips and the sample 
geometry must be applied as 

R = Y*F (1.5) 

where R is the sheet resistance, V is the measured voltage, I is the applied current, and F 
is the correction factor. 

The Hall effect is often used to measure the carrier density in the sample. Along with 
the resistivity, knowing the carrier density allows the calculation of the carrier mobility. 
The Hall effect is best explained with the use of Figure 1.5. Here, a current I x and a 
magnetic field B z are applied. Assuming the sample is p-type then the carriers are holes 
which have a positive charge. When the magnetic field is applied, the carriers, being free 
and charged, are influenced by the magnetic field and deflected in the y direction. This 
results in an accumulation of holes on one side of the sample and a depletion on the other. 



13 

This causes an electric field, Eh, to be generated in the y-direction which increases until 
it counteracts the effect of the applied magnetic field. Knowing the value of EyB z , and 
I x along with the Lorentz force expression, the carrier density can be determined [Li93]. 
Thus, according to Equation 1.4, the carrier density and the resistivity can be used to 
determine the Hall mobility. For p-type silicon at reasonably high concentrations 
(>5xl0 19 ions/cm 3 ), the Hall mobility measured does not equal the carrier mobility. To 
determine the actual mobility the Hall mobility must be divided by the Hall factor. 
Similarly, the carrier density found using Hall effect must be multiplied by the Hall factor 
to obtain the actual carrier density. A detailed description of the Hall factor can be found 
in many references [Li93, Li79, Lin81]. Essentially for low doping the Hall factor is 
generally assumed to be one and therefore the results from the Hall effect are reasonable. 
For heavier doping, the Hall factor drops below unity. The typical value used in 
converting the data is 0.7. Therefore, for this work the Hall effect measurements are 
converted using a Hall factor of 0.7. 
1.5.3 Structural 

Transmission electron microscopy (TEM) is a technique used to characterize the 
defect structure. TEM is a destructive technique requiring a sample thin enough to allow 
electrons to be transmitted through it. Sample preparation is slow and the resulting 
sample is very delicate. Great care must be taken not to damage the sample throughout 
the process. Detailed instructions on sample preparation can be found in earlier works 
from University of Florida graduates [Liu96, Mil99]. Once the sample is thinned, the 
sample is loaded into the vacuum chamber of the TEM. Basically, an electron beam is 
focused on the thin region of the sample allowing some of the electrons to be transmitted 
through the sample. This results in a directly transmitted beam and a diffracted beam. 



14 

Choosing a selected area of the diffraction pattern allows the user to obtain a dark-field 
image of the sample which will typically have higher resolution than the bright-field 
image. For plan-view imaging of the defects produced following anneals in implanted 
silicon, the g220 condition is used with a magnification typically 50,000 to 100,000 times 
the original size. 



15 



SDE 



.. 




Poly 
Gate 



Gate Dielectric 




■k 




EPITAXIAL LAYEI 



Lightly Doped Substrate 



Figure 1 . 1 Schematic of MOS transistor showing location of source drain extensions 
(SDE). 



16 



1 



c 
o 



35 
30 
25 
20 h 

15 r 

10 7 

5 - 



T 



"after Ins 
I "after 10ns 






1150 1200 1250 1300 1350 1400 1450 

Temperature (Celsius) 



0.06 r 



—•-Intrinsic Diffusion after Ins 
~* -B-I Enhanced Diffusion after Ins 
— *— Intrinsic B Diffusion after 10ns 
-•—B-I Diffusion after 10ns 




Figure 1.2 Top plot shows the average diffusion length of a silicon interstitial after 1 ns 
and 10 ns. The bottom plot shows the diffusion lengths for boron after 1 ns and 10 ns for 
intrinsic and transient enhanced (B-I Pair diffusion) diffusion. 



17 



2000 




1150 1200 1250 1300 1350 1400 1450 
Temperature (Celsius) 



Figure 1.3 The diffusion length of the silicon is divided by the diffusion length of the 
boron interstitial pair and plotted versus temperature. This shows how much farther a 
silicon interstitial can travel than a boron-interstitial pair at the same time and 
temperature. 



18 



3<t8nm, 15ns, 0.6J/cm2 



Icntfv-jJun; 1K1 




"lllA 

~70A 
"|(«1A 



2C»10- J *.l)»IO •' 60.10 * SUMO'-' |l. - 



Hn»(.» 



.«)8nm, 15ns,«.<iJ/cm2 




iJhiN 4 



Figure 1.4 This plot shows how fast the surface cools after reaching a peak temperature 
of 1600K (1327°C). The top plot shows how long it takes to cool to room temperature. 
The bottom plot shows how long it takes to cool to around 800°C. 



19 




f 



Figure 1 .5 Hall effect diagram. 



CHAPTER 2 
LASER ANNEALING 

2.1 Overview 

Understanding the effects of laser annealing on boron implanted silicon requires 
knowing where the energy is deposited during the irradiation and how that energy affects 
the silicon and boron in the lattice. Modeling the temperature distribution in the silicon 
during the laser anneal will help aid in understanding these effects. In this chapter, a 
model implemented in FLOOPS (Florida's Object Oriented Process Simulator) will be 
presented for the temperature distribution in the silicon during the laser anneal and during 
the cooling of the wafer after and between laser pulses. Ideally the temperature 
distribution versus depth could be used along with boron and defect models in FLOOPS 
to predict the boron diffusion and defect distribution following the NLA. This of course 
requires accurate modeling of the defect evolution and boron diffusion on nanosecond 
time scales. 

2.2 Laser Beam Interaction with Silicon 

The light from a laser is highly directional. Using lenses, the light can be focused and 
concentrated to a spot of any size. Unfortunately the light is also coherent which means 
it is capable of self-interference. This scattering can cause the beam intensity to vary 
across the irradiated leading to problems with uniformity. The lasers used in this study 
have a variation in energy of only 3%. The 308 nm laser can irradiate a 5 x 5 mm 2 
sample during one pulse, and the 532 nm laser a 1 x 1 cm 2 sample during one pulse over 
the energy density ranges used in this work. 

20 



21 

For the laser to interact with the silicon, it needs to transfer its energy to the lattice. It 
can do this by accelerating particles in the crystal. When those particles collide with the 
atoms in the lattice energy is transferred to the lattice via lattice vibrations, and heat is 
created. Laser wavelengths in the UV range result in electromagnetic fields with high 
frequencies. Since the atoms in the lattice are basically too heavy to respond 
significantly to these fields the energy is transferred from the field to the lattice by the 
electrons which, after being accelerated by the field, collide with the atoms in the lattice. 
Thermal equilibrium of the carriers occurs in less than 10 ps [W008I]. Of course the 
bound electrons respond weakly to the field compared to the free electrons which are 
easily accelerated by the field. The electrons that do not collide with the lattice re-radiate 
or reflect the energy without adding heat to the lattice. In other words, the photons 
generated by the laser are absorbed by the silicon through electron-hole excitations and 
other absorption mechanisms which results in thermal equilibrium of the carriers in less 
than 10 ps. For nanosecond pulses the plasma effects due to excited carriers are 
negligible [W008I]. 

2.3 The Temperature Model 

Because the heating occurs so rapidly and the laser energy is highly directional, the 
temperature gradients perpendicular to the surface are much greater than those parallel to 
the surface. Therefore, the temperature can be modeled using the one dimensional heat 
flow equation: 

p • Cp • d T/dt = 5/dx(K • dVdx) + Io • (1 - R) • a • e " a ' X (2.1) 

2 
where I is the intensity of the laser (W/cm ), R is the reflectivity, a the absorption 

coefficient, x the depth in to the crystal (perpendicular to the surface), K is the thermal 



22 

3 
conductivity, C p is the heat capacity (J/g°C), and p is the material density (g/cm ). The 

variables p, C p , K, a, and R are all temperature dependent. However, p is set to 2.33 
g/cm 3 for all simulations. To properly model the cooling of the wafer, the radiation of the 
heat from the surface (x=0) and back-side (x=d) of the wafer is accounted for with the 
following equation: 

d T/3t | x =o, d = - (A • e • a • T 4 ) / (m • Cp) (2.2) 

where A is the surface area of the sample, e is the emissivity (0.4), and o is the Stefan- 
Boltzmann constant (5.67e-12 W/cm 2 -K 4 ), and m is the mass (p • sample volume). 

These equations require knowledge of the absorption coefficient and reflectivity of the 
boron implanted silicon at the lasers output wavelength as well as how it varies with 
temperature. However, for these models the optical properties used are determined from 
measurements made on crystalline silicon. Data for the boron-implanted silicon versus 
temperature is not available. The following equations are analytical fits for the 
temperature dependent optical properties: 

C p (T) = 24.236 + 2.344e-3 • T - 4.56e-5 • T 2 (2.3) 

K(T) = 90.065 • 1 .Oe-4 / (T-300.0) (2.4) 

a(T) = 2.26e-3 • exp(2.26e-3 • (T - 300.0)) (2.5) 

R(T) = 0.382 + 4.0e-5 • (T - 300.0) (2.6) 

The optical properties of crystalline silicon can be found in many publications [Jel82, 
Hil80, Zha96]. Using this model the temperature distribution in silicon can be estimated. 
Similar results can also be obtained by setting the parameters to constant values. In this 
case, Cp is set at 0.7 J/g-C, K at 1.6 W/cm-C, a at 125.0 cm" 1 , and R at 0.4. Figure 2.1 
shows how the temperature varies over time at various depths for the 308 ran laser during 



23 

one 15 ns laser pulse at 0.6 J/cm 2 . Figure 2.2 shows how the temperature varies over 
time at various depths for the 532 nm laser during one 20 ns laser pulse at 0.35 J/cm . 
Figure 2.3 shows the heating and cooling of the surface for 3 laser pulses at a frequency 
of 100 Hz using the 532 nm laser at 0.35 J/cm 2 with a pulse length of 20 ns. Figure 2.4 
shows the magnified regions of the plot in Figure 2.3. A complete description of this 
temperature model along with the FLOOPS files can be found in Appendix A. 

2.4 Laser Interaction with Implanted Silicon 

When the light in the UV range hits the silicon it interacts with the electrons and those 
electrons collide with the atoms which transfers energy to the lattice and heats the crystal. 
In a perfect crystal, the resulting temperature distribution would follow equation 2.1. 
However, when the crystal has defects, those defects add to the number of electrons 
which can affect the way the energy is distributed in the crystal. 

To make Equation 2.1 more physically accurate the absorption coefficient, thermal 
conductivity, and reflectivity must all be made dependent on the free carrier distribution 
and the temperature of the silicon. Unfortunately, optical data does not yet exist for the 
conditions needed. Optical measurements would need to be made on the silicon which is 
heavily doped with boron during the laser anneal for optimum results. 

Using Equation 2.1 gives a rough idea of how the temperature is distributed in the 
silicon. Knowing that the laser radiation couples more with the loosely bound valence 
electrons gives further insight into how the light will couple to ion implanted silicon. 
After the implant the boron and the damage result in an increase in the number of loosely 
bound electrons near the samples surface. This distribution of electrons should influence 
how the energy is transferred and heat distributed during a single laser pulse. This would 
mean that areas where the damage and boron is located could result in an increase in the 



24 

density in that region causing more of the energy to be deposited in that region. This 
could theoretically decrease the absorption depth of the laser. 
2.4.1 Absorption Depth and Implant Energy 

How far the silicon interstitials can move is highly dependent on where the silicon 
interstitials are in relation to the heating resulting from the absorption of the laser. The 
absorption depth of the laser gives information on the maximum depth heated by the 
laser. For example, if the implant damage is located deeper than where the energy is 
absorbed, not much diffusion will occur. Take the following cases: A) a laser has an 
absorption depth of 70 A and the projected range of the implant is at 700 A, B) a laser has 
an absorption depth of 70 A and the implant as a projected range of 20 A. For case A, the 
bulk of the damage which is near the projected range will not be affected by the laser 
anneal. For case B, the bulk of the damage is at 20 A which is within the region heated 
by the laser. Figure 2.1 and 2.2 shows how the temperature varies versus time over 
various depths. The lasers used in this work are a 308 nm excimer laser and a 532 nm 
RubyrYAG laser. The absorption depth for the 308 nm in crystalline silicon is around 70 
A. The absorption depth is around 8000 A for the 532 nm laser. Picking implant 
conditions which keep the bulk of the damage and the implant within the absorption 
depth of the laser used will allow the entire implanted region to be annealed during the 
NLA. However, due to the way the temperature distributes in the wafer (Figures 2.1 
and 2.2) the shallower implants will always see average temperatures higher than deeper 
implants even when both are within the absorption depth of the laser. 
2.4.2 Silicon Interstitial and Boron Diffusion during Annealing 

As shown in Chapter 1, silicon interstitial diffusivity in silicon increases as the 
temperature increases according to the following equation: 



25 

_. -Ea/kT 

D - Do • e (2.7) 

Using Equation 2.7 it can be found that in 10 ns a silicon interstitial can diffuse 16 A at 
1200°C and 32 A at 1400°C. This means that during a single 15 ns pulse interstitials can 
begin to move to the surface or evolve into clusters. If the interstitials should start to 
cluster, sub-microscopic interstitial clusters (SMICs), 12 defects, 311s, and loops could 
form. 

Boron also diffuses according to Equation 2.1. However, as shown in Figures 1.2 and 
1.3, it can be shown that the boron- interstitial pair diffusion at 1200°C is around 1000 
times slower than the silicon interstitial. This means that it would take around 1000 times 
the number of laser pulses to move the boron the same distance as the silicon interstitials 
move in one pulse. This also explains why it is possible to remove most of the implant 
damage without causing significant boron diffusion when a high-temperature anneal is 
applied to an implanted region for a short time. 

When using the NLA technique, it is important to select the appropriate laser for the 
NLA. For example, Figure 2.5 shows the boron profile after a 5 KeV, 2el5 ions/cm 2 
implant. It also shows the region which is heated during a 308 nm NLA. As shown, only 
7% of the implanted layer is annealed during a 308 nm NLA where 100% is heated for a 
532 nm NLA. This is because the absorption depth of the 308 nm laser is around 70 A 
while the 532 nm laser has an absorption depth between 5000 and 10000 A. This means 
that the 308 nm NLA is more effective for implant energies around 1 KeV or less and the 
532 nm NLA for implant energies up to 5 KeV. In the following chapters, the implant 
energy has been varied to show the effect of the laser's absorption depth on the boron 
diffusion and defect evolution. 



26 

2.4.3 Increasing the Number of Laser Pulses 

Removing the damage after the implant requires annealing the implanted region. The 
time and temperature that the damaged region sees will determine how much damage 
remains in the crystal and how much the boron will diffuse. During one nonmelt 15 ns 
laser pulse, there is time for the silicon interstitials to move around but perhaps not 
enough time for all of the damage to be removed. To remove more damage it seems that 
it would be ideal to increase the length of the laser pulse. Increasing the length of the 
laser pulse however results in an increase in the temperature that the surface reaches. 
According to the temperature model presented in Chapter 1, a 0.1 ms pulse at 0.6 J/cm 2 
would raise the surface to a temperature greater than the melting point of silicon 
(~1410°C) most likely vaporizing the region. Of course, the temperature model in 
Chapter one does not account for the phase change in the material that occurs at melting, 
so calculating actual temperatures above the melting point of silicon is not reasonable. 
Therefore, instead of increasing the length of the pulse, the damage can be removed 
little by little by simply increasing the number of pulses. If the time between pulses is 
long enough for the sample to cool back to room temperature, the surface temperature 
should never exceed the temperature seen during the first pulse. Although the laser heats 
just the surface during the pulse, the heat distributes through the bulk via thermal 
conductivity. During subsequent pulses, if bulk heating occurs more boron or silicon 
diffusion than that seen during the first pulse will occur due to the increase in temperature 
over the region. Also, the initial temperature of the wafer determines the peak 
temperature reached during the NLA with higher initial temperatures increasing the final 
surface temperature. Bulk heating can be avoided by adjusting the pulse frequency of the 
laser. 



27 

2.5 Determining the Melting Point 
These initial experiments are designed to determine the melting point of the silicon 
surface. To investigate the effects that nonmelt laser annealing has on boron diffusion 
and defect evolution, experiments are performed which vary the laser energy density 
during the NLA. Experiments are performed using both the 308 ran laser and the 532 nm 
laser. 
2.5. 1 The 308 nm Melting Point 

To ensure that the regions studied will not be melted, an initial set of experiments is 
performed using the 308 nm laser. For this set of experiments, 0.5 by 0.5 cm 2 silicon 
samples each implanted with 10 15 B+ ions/cm 2 at 5 KeV are used. Each sample is 
irradiated at a given energy density with one pulse. For the 308 nm laser, the laser 
energy density is varied from 0.35 to 0.75 J/cm 2 and the pulse length is 15 ns. During 
each laser anneal, a HeNe laser is bounced off the surface of the sample to measure 
reflectivity. The reflectivity plateaus when the surface melts. For these samples, the 
plateau is at 0.7. After all of the samples are annealed the sheet resistance of each sample 
is measured using a four-point probe. Plots of the sheet resistance versus laser energy 
density along with the point when the surface reflectivity plateaus show the maximum 
energy density which can be used to perform non-melt laser annealing. 

The results for the sheet resistances versus laser energy density using the 308 nm laser 
and for the reflectivity versus laser energy density are shown in Figures 2.6 and 2.7 
respectively. As you can see in the figures, the crystalline silicon melts at around 0.62 
J/cm 2 when one 15 ns pulse from the 308 nm laser is used. The 15 ns pulse length is 
chosen because the laser used is more stable for this pulse length. Increasing the pulse 
length will increase the amount of radiation that the sample receives. This will cause the 



28 

temperature to be higher for the longer pulses length. Therefore, for longer pulse lengths 
lower energy densities will need to be used to keep the sample from melting. 
2.5.2 The 532 nm Melting Point 
For the 532 nm experiments, to ensure that the regions studied will not be melted, an 
initial set of experiments is performed using the 532 nm laser. For this experiment, 1 by 

2 i ^ o 

1 cm silicon samples implanted with boron at a dose of 2x10 ions/cm and an energy 
of 5 KeV are used. Each sample is irradiated at a given energy density with one pulse. 
For the 532 nm laser, the energy density is varied from 0.29 to 0.40 J/cm 2 and the pulse 
length is set at 20 ns. After all of the samples are laser annealed, the sheet resistance of 
each sample is measured using a four-point probe. Plots of the sheet resistance versus 
laser energy density along with the point when the surface reflectivity goes to one show 
the maximum energy density which can be used to perform nonmelt laser annealing. 

The results for the sheet resistances versus laser energy density using the 532 nm laser 
are shown in Figure 2.8. The reflectivity versus laser energy density is plotted in Figure 
2.9. The crystalline silicon melts at around 0.37 J/cm 2 when one 20 ns pulse from the 
532 nm laser is used. 



29 



308nm. 15ns. 0.6J/cm2 




50x10 



1.0*10 -* 



t.5xl0 * 



lllWl.l 



Figure 2. 1 This plot shows the temperature versus time seen at various depths in the 
wafer during the NLA. The top curve is the temperature at the surface of the wafer. The 
bottom curve is the temperature at 100 A into the wafer. 



30 



532nm, 20ns, 0.35J/cm2 



Tcmpi.K) 




000 



J 

5.th!0-" 1.0*10-' 1.5x10 



* :o«io s 2.5*10 -* 



Tin»:.>i 



Figure 2.2 This figure shows the temperature distribution in the wafer during one 20ns 
pulse with the 532 nm laser. It also shows the beginning of the cool down after the pulse 
is turned off (time > 2.0xl0" 8 s). 



31 



532nm, 20ns, 100Hz, 0.35J/cm2 



Tcrapetaiwr iKxWinj 



1.6jtO 




5.0x10 



1*10 " J 2.0*10 " 2 2S»I0' J JOxlO- 2 



Time M 



Figure 2.3 This plot shows the temperature versus time seen at the surface of the wafer 
when the sample is irradiated with multiple pulses at a frequency of 100Hz. 



32 



532nm, 20ns, 100Hz, 0-35J/cm2 



Tcmrcr^ttrc iKelvui] 
T 



IS»10 




IIKIO • 



Tin: i.i 



532nm, 20ns, 0.35J/cm2 



Tcnp.Kl 




5<hlO 



2i)»J0 



Time is) 



Figure 2.4 These plots are magnified views of the plot in Figure 2.3. This shows a more 
detailed view of how the temperature is distributed over depth during the 532nm NLA. 



33 



ro 



a 



2 

O 



irtion of profile annealed during the 
$08 nn\anneal 




MA 



1000 1500 2000 2500 3000 



Depth (A) 



Figure 2.5 Illustration of the approximate amount of the 5 KeV boron implant which is 
annealed during a 308 nm NLA. The entire area is annealed during a 532 nm NLA. 



34 



2500 




Laser Energy (J/cm ) 



Figure 2.6 Sheet resistance vs laser energy density in 5 KeV, lei 5 B+/cm2 samples 
irradiated with one 15 ns pulse using the 308 nm laser. 



35 



0.8 
0.7 
0.6 



i 



0.5 
0.4 



0.3 



0.2 



J I I I I I L 



0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 

Laser Energy Density (J/cm 2 ) 



Figure 2.7 Reflectivity versus laser energy density after one pulse with the 308 nra laser 
on 5 KeV, 2el5 B+/cm2 samples. 



36 



1500 



a 



a 

« 

• !■< 

a* 



1000 - 




500 - 



Laser Energy Density (J/cm ) 



Figure 2.8 Sheet resistance versus laser energy density for the 5 KeV, 2el5 B+/cm2 
samples following one 20 ns pulse with the 532 nm laser. 



37 




Laser Energy Density (J/cm ) 



Figure 2.9 Reflectivity versus laser energy density for 5 KeV, 2el5 B+/cm samples 
annealed with the 532 nm laser using a 20 ns pulse 



CHAPTER 3 

EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON 

IMPLANTED SILICON: 308 NM EXCIMER LASER 

3.1 Overview 

The main focus of this work is to investigate the effects of laser irradiation on boron 
implanted crystalline silicon under conditions that do not cause melting of the implanted 
region. How the laser affects the implanted region can be characterized by determining 
the following: how the boron diffuses, how much of the boron becomes active, and how 
the damage evolves during the laser anneal and with post-processing after the laser 
anneal. These parameters have been shown to be dependent on the output wavelength of 
the laser, the laser energy density of the incident beam, the length of the laser pulse, and 
when multiple pulses are used, the time between pulses. Also of importance is the depth 
of the damage and the boron during the laser anneal. 

Since the laser energy densities where NLA can be performed have been determined 
(Chapter 2), further experiments can now be carried out without worrying about melting 
the silicon. This chapter (Chapter 3) and Chapter 4 give the experimental results and a 
discussion of the results for samples annealed with the 308 nm laser and the 532 nm 
laser, respectively. Chapter 5 elaborates on the effects of NLA on boron diffusion and 
defect evolution by analyzing the effects of post-processing on samples given an NLA. 



38 



39 

3.2 Experiments 

3.2.1 Increasing the Number of Laser Pulses: 308 nm Laser. 5 KeV Boron Implant 
A 5 KeV, 2el5 B+ ions/cm 2 implant into a CZ grown <100> silicon wafer is 

processed with a 308 nm XeCl excimer laser using one to 100 15 ns pulses at a laser 
energy density of 0.6 J/cm 2 . Control samples receive an RTA step for 5 sec at 1040 °C 
instead of the laser annealing. Indium contacts are made to the samples for sheet 
resistance measurements using the Hall effect system. These samples are all analyzed 
using SIMS, Hall Effect, and Plan-view TEM. 

3.2.2 Increasing the Number of Pulses: 308 nm Laser. 1 KeV Boron Implant 

A 1 KeV, 10 15 ions/cm 2 B+ implant into a CZ grown <100> silicon wafer is processed 
with the 308nm XeCl excimer laser. The 1 KeV implants received one or ten 15 ns 
pulses at a constant energy density of 0.55 J/cm 2 . Following the NLA some samples 
receive an RTA for 5 sec at 1040 °C. Control samples received the RTA and no NLA. 
These samples are then analyzed using SIMS, Hall effect, and plan- view TEM. Indium 
contacts are used for the Hall effect measurements. 

3.3 5 KeV Results and Discussion 

In order to investigate the effect that varying the number of laser pulses has on an 
implant that is predominately deeper than the lasers absorption depth, an experiment 
using the 308 nm laser is performed on samples implanted with boron at 5 KeV. This 
experiment is described in section 3.2.2. The samples that receive the NLA are compared 
to samples that just receive an RTA at 1040 °C 

Figure 3.1 shows the SIMS profiles of the boron as-implanted, following the NLA, 
and after the RTA. SIMS of the samples which received the NLA were the same as the 
as-implanted profile showing that no detectable movement in the boron profile occurred 



40 

following the NLA when compared to the as-implanted profile. At a boron concentration 
of 10 18 ions/cm 3 , the boron moves 200 A during the RTA. 

Although no boron diffusion is detected in the SIMS, results show the sheet resistance 
drops as the number of laser pulses increases with the most significant drop occurring 
between 10 and 100 pulses (Figure 3.2). Thus, the NLA alone results in a sheet 
resistance of 84 Q/sq after 100 pulses compared with 520 Q/sq in the sample just 
receiving the RTA. 

Figure 3.3 shows the plan- view TEM of the 5 KeV, 2el5/cm 2 implants following 
NLA and following the RTA. After the one pulse the formation of many tiny defects 
begins to be detectable (top left picture). In this picture, a very grainy texture is observed 
which is different from the as-implanted sample which shows no texture (much as this 
TEM picture shows when printed). After ten pulses a high density of tiny dots become 
visible in TEM (top right picture). These dots are slightly larger than those formed after 
one pulse and the density appears to be slightly lower making it possible to note the 
formation of individual defects. These dots grow into slightly larger defects with the 
density decreasing again after 100 pulses (bottom left picture). As expected numerous 
large loops were nucleated following the RTA alone (bottom right). It is immediately 
obvious that the nonmelt laser anneal does not remove all of the damage from the 
implanted samples. This makes sense based on the fairly shallow absorption depth of the 
laser. The bulk of the damage and boron is well beyond the region that is heated by the 
laser. Although the NLA did not cause boron diffusion, it is shown through the TEM that 
the NLA alone has a very noticeable effect on the silicon interstitial diffusion. Thus the 
NLA causes the nucleation of numerous tiny defects during one 15 ns laser pulse. 



41 

Examining the diffusion length of silicon interstitials over the temperature range from 
1200-1400°C gives insight into why the interstitials have time to cluster during the 15 ns 
anneal although the boron diffusion is minimal (Chapter 1). Since the boron is not 
diffusing and causing an increase in width of the layers, the question remains as to why 
the sheet resistance is decreasing during the NLA. In Chapter 6, the mobility and 
activation of the layer is investigated. Understanding what causes the changes in the 
mobility and activation will explain the drop in sheet resistance. 

3.4 1 KeV Results and Discussion 

Realizing that the 5 KeV implant produced a damage and boron profile far deeper than 
the absorption depth of the 308 nm laser, a shallower implant energy of 1 KeV is chosen 
for study. For this experiment, the effect of using multiple laser pulses is also studied. 
Since the NLA alone from a single pulse decreases the sheet resistance of the boron 
implanted layer without causing any boron diffusion, annealing the same area with more 
pulses should result in lower sheet resistances without causing much if any boron 
diffusion. 

Figure 3.4 shows the SIMS of the 1 KeV samples as-implanted, after 10 laser pulses, 
and after the 1040°C, 5 sec RTA. SIMS for the sample receiving one laser pulse is nearly 
identical to the as-implanted profile. SIMS for the sample receiving ten laser pulses 
shows that some boron diffusion occurs during the NLA alone. At a boron concentration 
of 10 18 ions/cm 3 the boron moves 130 A during the RTA. 

Figure 3.5 shows the change in sheet resistance as the number of laser pulses is 
increased for samples receiving the NLA and for the one receiving just the RTA. The 
results show that the NLA alone results in a decrease in sheet resistance. The decrease in 



42 

sheet resistance following the NLA occurs with little change in the junction depth which 
is measured at 10 18 ions/cm 3 (Figure 3.4). 

Plan- view TEM pictures of the 1 KeV boron after 10 laser pulses and after the RTA 
are shown in Figure 3.6. Figure 3.6 shows the NLA often laser pulses alone nucleates 
numerous small loops (left picture). Figure 3.6 also shows the TEM after the RTA alone 
(right picture). As is shown, the RTA results in fairly large loops compared to those 
formed after the NLA. This change in defect density is qualitatively similar to that for 
the 5 KeV samples. 

The variations in diffusion and size of defects nucleated between the 5 KeV and 1 
KeV samples can be attributed to the interaction of the laser beam with the damage and 
boron following the implant. The laser used has an absorption depth around 70 A. The 
peak of the boron as-implanted profile is around 260 A for the 5 KeV implant and 50 A 
for the 1 KeV implant. For the 1 KeV implant, the effect of the laser is distributed across 
the bulk of the damage and dopant profile. While for the 5 KeV implant, the laser 
interacts with less than a fifth of the damage and dopant profile. During the NLA the 
surface is heated to 1200-1400°C for a few nanoseconds. This allows time for the silicon 
interstitials to move around, but not the boron. 

Due to the fact that the 1 KeV implant damage is contained primarily within the 
absorption depth of the laser, the 1 KeV implanted samples will see higher temperatures 
during the NLA than the 5 KeV implanted samples. This higher temperature in the 1 
KeV results in the boron profile showing slight diffusion after 10 pulses at a boron 
concentration of 10 19 ions/cm 3 . Of course, this movement could also be attributed to 



43 

SIMS error. So perhaps the SIMS profiles do not provide a convincing argument that the 
1 KeV implant sees higher temperatures than the 5 KeV implanted samples. However, 
comparing the defect microstructures of the 5 KeV sample after 100 pulses with the 1 
KeV sample after 10 pulses, shows that the defects are very similar in size and density 
suggesting the 5 KeV sample sees the same average temperature as the 1 KeV samples 
after 10 times the number of pulses. 

3.5 Concluding Remarks 
Basically, these results are presented here to convince the reader that it is important to 
consider the absorption depth of the laser and how the temperature is distributed 
compared to the implant profile when designing an annealing process using NLA. Also, 
these results show that the NLA can be used to decrease the sheet resistance without 
increasing the width of the implanted region. Due to a change in the availability of the 
laser, a more complete study involving more laser pulses could not be carried out with the 
308 nm laser. However, for the next set of experiments a large amount of extra material 
is processed to account for any losses to the sample quantity occurring during sample 
preparation for the various destructive techniques used for analysis. That said, in the next 
chapter a similar set of experiments is performed using a 532 nm laser and one to 1000 
pulses. The 532 nm laser has an absorption depth of between 5000 and 10000 A in 
crystalline silicon compared to 70 A for the 308 nm laser. 



44 



10 



21 



a 

c 

o 
s« 

O 

PQ 



10 1 



10 J 



10' 



as-implanted + NLA 
0.0 J/cm2 w/RTA 




500 1000 1500 2000 

Depth (A) 



2500 3000 



Figure 3.1 SIMS of 5 KeV, 2el5 B+/cm2 samples as-implanted and after the NLA with 
308 nm laser, and after 1040°C,5 sec RTA. 



45 



3000 



9> 


2500 


03 




a 




c 


2000 


W 




U 




a 


1500 


a 




*•* 




•P* 




a 




OS 


1000 


1 




.4 


500 


</> 










1 10 

# of Laser Pulses 



100 



Figure 3.2 Sheet resistance number of laser pulses for 5 KeV, 2el5 B+/cm2 samples 
following an NLA with the 308 nm laser at 0.6 J/cm2. using a pulselength 1 5 ns and i 
frequency of 10 Hz. 



46 




O.^vm^ 



Figure 3.3 Plan-view TEM for 5 KeV, 2el5 B+/cm 2 samples following one pulse (top 
left), 10 pulses (top right), 100 pulses (bottom right), and after a 1040°C, 5 sec RTA 
(bottom right). For the NLA the 308 nm laser is used with a 15 ns pulse at a frequency of 
10 Hz and a laser energy density at 0.6 J/cm 2 . 



47 



10 



21 



1 ] 



2 

o 
10 



20 



19 



10 



18 



100 



as-implanted 
10 laser shots 
RTA only 



200 300 400 

Depth (A) 




Figure 3.4 SIMS of the 1 KeV, lei 5 B+/cm2 samples as-implanted, after ten pulses, and 
after a 1040oC, 5 sec RTA. The 308 nm laser with a 15 ns pulse at 10 Hz is used. 



48 









7000 



5f6000 
J 5000 

O 

o 4000 
9 

s 

^3000 

•M 
OB 


PSh 2000 
5 

-= 1000 

C/5 




# of laser pulses 



10 



Figure 3.5 Sheet resistance versus number of laser pulses for the 1 KeV, lei 5 B+/cm2 
samples using the 308 nm laser with a 15 ns pulse at 10Hz. The point at pulses 
represents the sample that just received the 1040°C, 5 sec RTA. 



49 




Figure 3.6 Plan-view TEM of the 1 KeV, lel5 B+/cm2 samples after 10 pulses using the 
308 nm laser with a 15 ns pulse at 10Hz (left) and after the 1040°C, 5 sec RTA(right). 






CHAPTER 4 

EXPERIMENTAL INVESTIGATIONS OF THE EFFECTS OF NLA ON BORON 

IMPLANTED SILICON: 532 NM RUBY:YAG LASER 

4.1 Introduction 
This set of experiments is designed to further investigate the effects of multi-pulse 
nonmelt laser annealing on non-amorphizing doses of boron implanted in silicon. For 
these experiments, a laser with a wavelength of 532 nm is used. This laser has an 
absorption depth of 5000 to 10,000 A which is nearly a thousand times deeper than that 
of the 308 nm laser. To show how the absorption depths affect the outcome of the NLA, 
the same 5 KeV implant used in Chapter 3 for the 308 nm NLA is also studied here with 
a 532 nm NLA. The SIMS profiles, sheet resistances, and plan-view TEM results after 
one to 1000 pulses are presented and compared to a conventional 1050°C spike anneal. 

4.2 Increasing the Number of Pulses: 532 nm Laser. 500 eV Boron Implant 
4.2.1 Experiment 

A 500 eV, 10 15 ions/cm 2 B+ implant into a CZ grown <100> silicon wafer is annealed 
with a 532 nm laser using one, 10, 100, and 1000 20 ns long pulses at an energy density 
of 0.35 J/cm 2 . Recall from Figure 2.9 that above 0.35 J/cm2 at around 0.37 J/cm 2 the 
reflectivity of the surface (measured with a HeNe laser) plateaus indicating that surface 
melting has occurred. The frequency of the laser is set at 100 Hz which allows time for 
the sample to cool between pulses. The laser irradiates an area 1 x 1 cm 2 with less than 
3% variation in the beam over that area. Also, for the 532 nm laser, the absorption depth 
into crystalline silicon is around 800 nm. These samples are compared to implanted 



50 



51 

samples receiving a conventional 1050 °C spike anneal without any NLA. All samples 
are analyzed using SIMS, Hall effect and plan-view TEM. 
4.2.2 Results and Discussion 

During a 20 ns pulse at 0.35 J/cm 2 , the temperature is expected to reach approximately 
1200-1400 °C 500 to 10,000 A deep into the sample while the bulk of the sample remains 
at room temperature. After the 20ns pulse, the bulk then acts as a heat sink for the 
surface region allowing the sample to cool down to below 500 °C in less than 0.1 ms. 
Since the projected range of the 500 eV boron implant is at 2.5 nm, the entire boron 
profile is expected to be heated during the NLA. 

SIMS of the boron profiles as-implanted, following the NLA, and following the spike 
anneal are shown in Figure 4.1. No diffusion is observed following one pulse. However, 
the profiles following 10, 100 and 1000 laser pulses do show slight diffusion as the 
profiles begin to break away from the as-implanted profile at a boron concentration 
around 10 ions/cm . Diffusion does not appear to occur in the tail region of the profile 
below 3xl0 17 ions/cm 3 resulting in 21 to 25 nm junctions at 10 18 ions/cm 3 . Although 
some of the boron diffusion does occur during the NLA alone, most of the diffusion 
occurs during the spike anneal resulting in the profile diffusing 170 A at 10 18 ions/cm 3 
resulting in a junction depth of 28 nm. 

The sheet resistance measurements shown in Figure 4.2 are determined using Hall 
effect measurements on square samples using indium contacts. Standard deviation for 
the sheet resistance values for each sample is between 2 and 6%. Sheet resistance drops 
to 800 Q/sq and remains at around the same value following 10 pulses or more with the 
NLA alone. The sheet resistance only drops to 2000 Q/sq after the spike anneal alone. 






52 

Figure 4.3 shows the plan-view TEM for the 500 eV samples after the 1050 °C spike 
anneal (bottom right). As shown, only a few loops 10-20 A wide exist after the RTA. 
Plan-view TEM of the samples following NLA show no defects. Since the NLA 
nucleates a high density of small defects, it is not believed that the NLA alone completely 
removes the implant damage but merely results in defects too small to detect with TEM. 
Post processing of these samples will give more information as to what type of defects if 
any remain after the NLA. Post-processing results are shown in Chapter 5. 

4.3 Increasing the Number of Pulses: 532 run Laser. 5 KeV Boron Implant 

4.3.1 Experiment 

A 5 KeV, 2 x 10 15 ions/cm 2 B+ implant into a CZ grown <100> silicon wafer is 
annealed with a 532 nm laser using between one and 1000 20 ns long pulses at an energy 
density of 0.35 J/cm 2 . These samples are compared to a sample that received the more 
conventional 1050 °C spike anneal. SIMS, sheet resistance, Hall measurements, and 
plan-view TEM are made on all samples. 

4.3.2 Results and Discussion 

Recall that since the projected range of the 500 eV boron implant is at 26 nm, the 
entire boron profile is expected to be heated during the NLA. However, since the 5 KeV 
implant is roughly 10 times deeper than the 500 eV implant the average temperature over 
the region is expected to be less than that seen by the shallower implant. Boron profiles 
measured with SIMS of the as-implanted, laser annealed, and the one processed with the 
1050°C spike anneal are shown in Figure 4.4. No diffusion is observed following one, 
10, 100, or 1000 pulses while substantial diffusion occurs in the sample receiving just the 
spike anneal. These results are as expected since during the NLA the boron does not gain 
enough energy from the temperature seen during the 20 ns pulse to diffuse any 






53 



measurable distance. Where, during the spike anneal, the boron does obtain enough 
energy to diffuse. 

The implant damage does however receive enough energy to diffuse during the NLA. 
Figure 4.5 shows how the damage evolves as the number of laser pulses increases. The 
top left picture is after one pulse, the top right after 10 pulses, the middle left after 100 
pulses, the middle right after 1000 pulses, and the bottom picture after the 1050°C spike 
anneal. Once again, although the boron does not diffuse, the silicon interstitials cluster 
and form numerous tiny defects during the first pulse and those clusters grow into larger 
defects as the number of pulses increases. 

The sheet resistance measurements shown in Figure 4.6 are determined using Hall 
effect measurements on square samples using indium contacts. Standard deviation for 
the sheet resistance values for each sample is between 2 and 10%. The sheet resistance 
drops to less than 100 Q/sq during the NLA alone. It is interesting to note that the sheet 
resistance does not continue to decrease after 100 laser pulses. This result can be 
explained by examining the mobility and activation which is done in chapter 6. 

Figure 4.7 shows a plot of the sheet resistance versus junction depth for the 500 eV 
and 5 KeV experiments with the NLA compared to results from conventional processing 
with the spike anneal. As shown, NLA will allow the formation of shallower junctions 
with lower sheet resistances than conventional processing techniques. 



54 



CO 

a 

(J 

= 

£ 

o 




200 300 
Depth (A) 



500 



Figure 4.1 SMS of the boron profiles as-implanted, following the NLA, and following 
the 1050°C spike anneal for the 500 eV, lei 5 B+/cm 2 samples. 



55 



3000 



9 




tt 


2500 


& 




a 




JZ 







2000 


w 




v 




<j 




d 


1500 


OS 




•w 




«5 




• — 




(/> 




o 


1000 


2 




-w 




u 






500 


CZ5 





1 



1 



_L 



1 10 100 

# of Laser Pulses 



1000 



Figure 4.2 Sheet resistance versus number of laser pulses for 500 eV, lel5 B+/cm 
samples annealed with the 532 nm laser at 0.35 J/cm 2 using a 20 ns pulse. 



56 




Figure 4.3 Plan-view TEM of the 500 eV, lel5 B+/cm 2 samples annealed with a 1050C 
spike anneal. 



57 



10 J 



J_I 







I ■ ■ ■ ■ I I ■ 

as-implanted and 
1, 10, 100, 1000 shots 

RTA only 




l_i i i i I i J 



500 1000 1500 
Depth (A) 



2000 



Figure 4.4 SIMS of the boron profiles as-implanted, following the NLA, and following 
the spike anneal for the 5 KeV, 2el5 B+/cm 2 samples. 



58 








Figure 4.5 Plan-view TEM of the 5 KeV, 2el5 B+/cm 2 samples annealed with the 532 
nm laser at 0.35 J/cm 2 using one, 10, 100, and 1000 pulses at 100Hz and 20 ns/pulse. 



59 



3000 



-5 




,5« 


2500 


E 




JS 




O 


2000 


'W 




V 




u 




= 


1500 


a 




+■> 




1 




J 


1000 


^ 




_ 






500 


35 






1 10 100 

# of Laser Pulses 



1000 



Figure 4.6 Sheet resistance versus number of laser pulses for 5 KeV, 2el5 B+/cm 2 
samples annealed with the 532 nm laser at 0.35 J/cm 2 using a 20 ns pulse. 



60 



a 4 
ISs 2000 

s 

M 

o 

t 1500 

g 

42 

.a iooo 

■9 

I 

? 500 

Xil 



- 


1 




1 1 


1 




I 


■ 

• 


1050°C spike anneal 
NLA only (100 pulses) 


- 








- 




... 






■ 


:J 


[ 




5keV 


- 


- 


1 




1 #1 


1 







50 



100 



150 



200 



250 



X j (nm) 



Figure 4.7 Sheet resistance versus junction depth comparing NLA and the conventional 
spike anneal for a 500 eV and a 5 KeV boron implant. 



CHAPTER 5 
EFFECTS OF POST-PROCESSING AFTER NONMELT LASER ANNEALING 

5.1 Overview 

This chapter shows and discusses the effects on boron diffusion and damage evolution 
of post-processing of the NLA samples with rapid thermal anneals and furnace anneals. 
After the NLA defects remain in the sample which are not visible in plan-view TEM. 
Annealing the samples for longer times will allow the defects remaining after the NLA to 
one, some, or all or the following: grow into defects (visible or submicroscopic), 
recombine at the surface, recombine in the bulk, cluster with the boron, and/or enhance 
the boron diffuse. Examining the defect structures and boron diffusion after post- 
processing the samples which receive an NLA makes it possible to characterize and 
further understand the types of defects that evolved during the NLA. 

The time and temperature of the post-anneals all affect how the defects will evolve 
and how the boron will diffusion. Device fabrication may also require various anneal 
step following the NLA. Therefore, high temperature rapid thermal anneals and furnace 
anneals are investigated. 

52 High-Temperature Rapid Thermal Annealing after 308 nm NLA 
5.2.1 Experimental Overview 

A 5 KeV, lel5 ions/cm B+ implant in silicon is processed with a single 15 ns laser 
pulse at varying energies, 0.40 to 0.6 J/cm 2 , with the 308 nm laser. To help determine the 
amount of remaining damage, some samples processed with the NLA also receive an 
RTA for 5 sec at 1000 °C. Also, a 1 KeV, lel5 ions/cm 2 B+ implant in silicon is 

61 



62 

processed with one or ten 15 ns laser pulses at a constant energy density of 0.55 J/cm 2 . 
The 1 KeV implants processed with the NLA are also given a 1040°C, 5 sec RTA. This 
allows us to observe the effects of using a laser anneal as a pretreatment for conventional 
processing. These results are compared to a sample that just receive the RTA. The 
samples are all analyzed using SIMS, Hall, and plan-view TEM. 
5.2.2 5 KeV Results 

Figure 5.1 shows the SIMS profiles of the boron as-implanted, following the RTA, 
and after the NLA and RTA for the 5 KeV implants. A comparison of the SIMS between 
the samples receiving just the RTA and the samples receiving the NLA and the RTA 
shows the junction depth increases from 0.16 to 0.18 urn with very little difference in 
diffusion for the NLA from 0.4 J to 0.6 J/cm 2 . The junction depth is measured at a boron 
concentration of 10 18 ions/cm 3 . 

Figure 5.2 shows a plot of the sheet resistance versus laser energy density for the 5 
KeV implants. Results show the sheet resistance drops to around 150 ft/sq for samples 
receiving the NLA and the RTA compared with the samples just receiving the RTA. This 
30% drop in sheet resistance comes with only a 10% increase in the junction depth. 

In order to understand the reasons for the boron diffusion and drop in sheet resistance, 
the samples are analyzed using plan-view TEM. For the 5 KeV implants, samples 
receiving the RTA, plan-view TEM results show the NLA strongly affects the extended 
defect density producing a larger density of smaller defects (Figure 5.3). For comparison, 
plan-view TEM following just the 0.4 J/cm 2 (top left) and 0.6 J/cm 2 (top center) NLA are 
also shown. The formation of numerous small defects (represented by the white dots) 
following the 0.4 J/cm 2 and 0.6 J/cm 2 NLA shows the dramatic effect of the laser 
preanneal on the defect nucleation. Figure 5.3 shows the defect evolution in samples 



63 

receiving the NLA at various energies followed by the RTA. The top right picture is for 
the sample receiving just the RTA and no NLA. It shows the formation of numerous half 
loops. (Half loops are loops that unfault on the surface.) The bottom pictures from left to 
right are for the samples which receive the 0.4 J/cm 2 NLA followed by the RTA, the 0.5 
J/cm 2 NLA followed by the RTA, and the 0.6 J/cm 2 NLA followed by the RTA. From 
these pictures, the number of the loops which extend to the surface (the half loops) is 
shown to decrease as the laser energy is increased. Note that the half loops have a nearly 
constant diameter around 0. lum for all four samples. Figure 5.4 plots the percentage of 
half loops extending to the surface versus laser energy. 

Also from Figures 5.3 it is shown that as the laser energy increases the density of the 
defects increases while the size of the defects decreases. This is quantified in Figure 5.5 
which shows the density of the defects versus laser energy. Recall that there is a drop in 
sheet resistance beyond that expected due to the increase injunction depth. This drop in 
sheet resistance must be due to an increase in mobility or an increase in carrier activation. 
Since from Figures 5.3 and 5.5, the number of defects visible in plan-view increases it is 
not immediately obvious why there would be a drop in sheet resistance unless it is due to 
an increase in activation. More defects would typically be expected to cause a decrease 
in the mobility which would increase the sheet resistance. A possible explanation at this 
time may be deduced from the previous figures. Recall from Figure 5.3 that as the 
number of defects increases the average size of the defects decreases resulting in fewer 
larger defects that extend to the surface. It is possible that the loops which unfault on the 
surface have scattering sites along the entire area (jtr 2 ) of the defect making the number 
of scattering sites proportional to r 2 . However, the smaller more perfect loops will have 



64 

scattering sites only along their circumference (2itr) making the number of scattering 
sites proportional to r. Hence, less scattering sites exist after the NLA resulting in an 
increase in the mobility. It is also possible that the loops which exist at around the 
projected range of the boron implant have little effect on the mobility compared to the 
effects of ionized impurity scattering or neutral scattering. The effects of the loops on 
mobility and activation will be investigated further in Chapters 6 and 7. 
5.2.3 IKeV Results 

SIMS for the 1 KeV implants are shown in Figure 5.6. SIMS following an NLA of 10 
pulses with no RTA is also shown for comparison. For the 1 KeV implants, SIMS of the 
samples receiving one laser pulse plus the RTA is nearly identical to the RTA alone. 
Figure 5.6 shows that the NLA often laser pulses prior to the RTA decreases the boron 
diffusion while one laser pulse shows no noticeable effect. This is contrary to the 5 KeV 
SIMS results which show that the boron profile diffuses more when given an NLA prior 
to the RTA, SIMS results of the 1 KeV boron show that the 10 pulses with the NLA prior 
to the RTA actually decreases the boron diffusion. 

Figure 5.7 shows the change in sheet resistance as the number of laser pulses increases 
for samples receiving the NLA followed by the RTA for the 1 KeV implants. The results 
following the NLA alone are presented for comparison. The sheet resistance following 
the RTA alone is 1 100 Q/sq. It drops to 220 Q/sq when receiving the 10 pulse NLA 
prior to the RTA. 

Plan- view TEM pictures of the 1 KeV boron after 10 laser pulses, after the RTA, and 
after 10 laser pulses plus the RTA are shown in Figure 5.8. The left picture shows that 
the NLA often laser pulses alone nucleates numerous small loops. The picture on the 



65 

right shows that the ten pulse NLA prior to the RTA reduces the final loop density when 
compared with the RTA alone (center picture). This change in defect size is qualitatively 
similar to that for the 5 KeV samples. However, the NLA prior to the RTA results in an 
increase in the loop density for the 5 KeV samples and a decrease in the loop density for 
the 1 KeV samples. 

The variations in loop densities and diffusion can be attributed to the interaction of the 
laser beam with the damage and boron following the implant. Recall, that the laser used 
has an absorption depth around 70 A. The peak of the boron as- implanted profile is 
around 260 A for the 5 KeV implant and 50 A for the 1 KeV implant. For the 1 KeV 
implant, the effect of the laser is distributed across the bulk of the damage and dopant 
profile. While for the 5 KeV implant, the laser interacts with less than a fifth of the 
damage and dopant profile. During the NLA the surface is heated to 1200-1400°C for a 
few nanoseconds. This allows time for the silicon interstitials to move around. Thus 
during one laser pulse interstitials diffuse to the surface where they recombine while 
some remain behind in clusters. 
5.2.4 Discussion 

In summary, for the 5 KeV implants we see that a laser preanneal does not anneal all 
of the damage from the implant. However, the NLA significantly alters the defects 
present after subsequent anneal and produces a decrease in sheet resistance as the laser 
energy density is increased. 

For the 5 KeV implant, during one laser pulse a region around 70 A thick rich in 
interstitials is heated resulting in the nucleation of numerous small interstitial clusters. 
When followed with an RTA, these interstitial clusters grow and act as traps for 
interstitials which would normally recombine at the surface. This increases the number 



66 

of interstitials available to contribute to TED and defect formation during post-annealing. 
As shown in Figure 5.1 similar diffusion occurs for all laser energies following the RTA. 
Also, although the number of loops increases as the number of laser pulses increases, the 
number of interstitials contained in the loops after the RTA is roughly the same for each 
sample (Figure 5.3). Since the bulk of the damage is not annealed during the NLA and a 
similar number of interstitials remain, post-processing of the samples receiving the NLA 
results in similar boron diffusion. 

For the 1 KeV, the bulk of the interstitials and boron are within 70 A of the surface. A 
possible scenario is that this high concentration of impurity atoms (which means more 
electrons) decreases the absorption length of the silicon reducing the depth of the heated 
layer. During the first laser pulse, numerous small defects are nucleated in this thin 
region with the size of the defect being no larger than the width of the heated region. 
During subsequent laser pulses the width of this heated region increases along with the 
size of the defects. After ten laser pulses the defects are large enough to be detected in 
the TEM. Meanwhile, during each pulse interstitials have been making it to the surface 
where they recombine resulting in fewer interstitials available to form loops and 
contribute to TED during post-annealing. 

5.3 High-temperature rapid thermal anneals after 532nm NLA 
5.3.1 Experimental Overview 

For these experiments, samples are implanted with either 500 eV, lei 5 B+ ions/cm 2 or 
5 KeV, 2el5 B+ ions/cm 2 . They are then given an NLA with the 532 nm laser. The 
energy density is set at 0.35 J/cm 2 . The number of pulses is varied from 1 to 1000. The 
samples are then post-processed with a conventional 1050 °C spike anneal. Results are 
compared to a sample with the same implant conditions that just receive the spike anneal. 



67 

5.3.2 5 KeV Results and Discussion 

For the 5 KeV samples, SIMS results show that the sample receiving one pulse plus 
the RTA diffuses slightly further than the sample which receives the RTA alone. The 
sample receiving 10 pulses plus the RTA diffuses about the same if not slightly less than 
the sample receiving just the RTA (See Figure 5.9). The samples receiving 100 or 1000 
pulses plus the RTA are shown to diffuse only slightly compared to the as-implanted 
profile. 

The sheet resistances versus number of laser energy pulses for the samples receiving 
the NLA plus the RTA are compared to the samples receiving just the NLA in Figure 
5.10. The sheet resistance at J/cm 2 on the NLA plus RTA line is for the sample 
receiving only the RTA. As shown, the sheet resistance decreases as the number of laser 
pulses increases and plateaus at around 150 Q/sq after 10 pulses. Also, for the sample 
receiving one pulse plus the RTA the sheet resistance actually increases while no 
improvement in the sheet resistance occurs in the samples receiving 10 or more pulses 
plus the RTA. The increase in sheet resistance for the sample receiving one pulse plus 
the RTA must be due to either a decrease in activation or mobility. This will be 
discussed in Chapter 6. 

Plan-view TEM for these 5 KeV implants processed with the NLA and RTA are 
shown in Figure 5.11. The upper left picture is for the sample which just receives the 
RTA, the upper right picture is following one pulse plus the RTA, and the bottom picture 
is following 10 pulses plus the RTA. The samples receiving 100 or 1000 pulses plus the 
RTA show no defects in plan-view TEM. It is interesting to note that similar SIMS 
profiles are obtained for all of the samples shown in Figure 5.11 although the defect 
structure is substantially different in each sample. 



68 

Since boron is believed to need to react with an interstitial to diffuse, having more 
interstitials available usually means more boron diffusion. This must mean that prior to 
or during the RTA, a similar number of free interstitials exist or are made available in 
each of the following samples: as-implanted, one pulse, and ten pulses. While since no 
diffusion occurs for the samples receiving 100 or 1000 pulses when processed with an 
RTA it appears that there are not any interstitials available to form mobile pairs and react 
with the boron during the RTA. Thus the defects visible after the 100 or 100 pulses NLA 
must have dissolved and recombined at the surface, formed microscopic interstitial 
clusters, or clustered with boron since they did not cause boron diffusion and are no 
longer visible in the TEM following the RTA. Since no loops exist in some of these 
samples, analyzing the boron activation for all of the samples should give information on 
what type of defects exist prior to the RTA. This will be discussed in Chapter 6. 
5.3.3 500 eV Results and Discussion 

For the 500 eV implants, SIMS results show that the boron diffusion is similar to the 
results for the 5 KeV implants (Figure 5.12). The sample receiving one pulse plus the 
RTA is nearly identical to the sample receiving the RTA alone while the sample 
receiving 10 pulses plus the RTA diffuses slightly less than the sample receiving only the 
RTA. The samples receiving 100 or 1000 pulses plus the RTA diffuse the least and only 
diffuse slightly when compared to the as-implanted profile. 

The sheet resistances versus number of laser pulses for the 500 eV implants processed 
with the NLA and RTA are presented along with the results just after the NLA in Figure 
5.13. For these samples, the RTA increases the sheet resistance. Since diffusion occurs 
during the RTA a decrease in the sheet resistance is typically expected. This change in 



69 

sheet resistance must be related to the changes in activation of mobility. This will be 
discussed in Chapter 6. 

The plan-view TEM of the samples after the RTA show no defects for any samples 
receiving the NLA prior to the RTA. The only sample which had any visible defects 
though few is the sample receiving just the RTA. The plan-view TEM picture for the 
sample receiving just the RTA is shown in Figure 5.14. There are at least two 
explanations as to why the defects are not visible in any of the plots except for the sample 
receiving just the RTA. The explanations do not conflict with each other and when used 
together further decrease the possibility of there being any visible defects. If 1000 pulses 
is enough to remover most of the damage for the 5 KeV implants, it is very likely that the 
NLA will remove most of the implant damage during 100 to 1000 pulses for the 500 eV 
samples. Interstitials in the 500 eV implanted sample should logically have around a 
tenth of the distance to travel to reach the surface as the 5 KeV implanted samples. 
Therefore, they should only need a tenth of the time to disappear. The other explanation 
for the lack of visible damage comes from analyzing the plan-view TEM for other 
samples processed with the NLA. It is shown in Figure 5.11 that the NLA causes a high 
density of smaller defects to evolve in samples. It is also shown that these defects are 
smaller on average in samples receiving the NLA prior to the RTA. So, if the defects are 
only 30 to 50 A in the 500 eV sample after only the RTA (Figure 5.14), then the defects 
would be even smaller and less likely to show up in TEM after the NLA. 

By looking at the SIMS for these samples more insight into the type of defects if any 
remain can be gained (Figure 5.12). Since the sample receiving one pulse plus the RTA 
diffuses about the same as the sample receiving just the RTA it is most likely that one 



70 

pulse does not remove much if any of the available interstitials. It merely allows it to 
form tiny clusters. Ten pulses prior to the RTA results in less diffusion compared to the 
RTA, so this means less interstitials are probably available to add the TED. These 
interstitials could have recombined at the surface, clustered with the boron, or clustered 
into more stable microscopic interstitial loops so as not to be available for boron diffusion 
during the RTA. Since the samples receiving 100 and 1000 pulses prior to the RTA 
diffuse only slightly into the sample, it appear that very few free interstitials exist 
following the 100 and 1000 pulse NLA. Once again, the defects could be hanging out in 
clusters instead of running to the surface to recombine. However, it is believed that most 
of the interstitials have diffused to the surface during the NLA. The few that remain most 
likely make it to the surface during the RTA. Further processing and SIMS analysis of 
these samples at lower temperatures for longer times would give even more detail as to 
how many interstitials remain, but this will be left for possible future studies. 

One point which has been left out of the discussion of the 500 eV samples is the dose 
loss which occurs during the RTA. Although the tails of the 5 KeV and 500 eV profiles 
diffuse similarly, the 500 eV samples exhibit serious dose loss with the average dose 
dropping 50% during the RTA. Since the boron has to go somewhere, the dose loss 
during the RTA must result in a pile up of the boron at the silicon/oxide interface and/or 
and increase in the boron in the oxide. For the sample receiving just the RTA or one 
pulse plus the RTA there would be interstitials around to enhance the diffusion. 
However, for the samples receiving 100 and 1000 pulses the interstitial population should 
be reduced enough so that which is typically called transient enhanced diffusion (TED) is 
dramatically reduced if not eliminated. So, if the interstitials which cause TED are gone, 



71 

then what drives the boron diffusion which results in the dose loss in the samples 
receiving 100 or 1000 pulses prior to the RTA? Perhaps, the phenomena call boron 
enhanced diffusion (BED) is occurring. The 500 eV implant does after all result in boron 
concentrations above le21 /cm 3 and one of the requirements for BED is a high 
concentration of boron. The diffusion behavior believe it or not helps explain the boron 
activation which occurs during the NLA and will be discussed in Chapter 6. 

5.4 Furnace Anneals and Damage Evolution 
5.4.1 308nm NLA 

These results are presented merely to further illustrate the dramatic effect that NLA 
has on defect evolution. The 5 KeV samples receiving the NLA with the 308 nm laser 
are post-processed using a 750°C furnace anneal from 15 to 90 minutes. The effects of 
NLA prior to furnace annealing on the defect microstructure are compared to samples 
which receive only the furnace anneal. The results from plan- view TEM are shown in 
Figure 5.15. The top left picture is for the 5 KeV sample processed with just a 750°C, 15 
min furnace anneal. The picture shows the formation of numerous 3 1 1 defects (the rod- 
like defects) and a few large dislocation loops. After 45 and 90 minutes none of the 3 1 1 
defects remain and only one or two large loops are visible in TEM. The upper right 
picture shows the defect evolution following the NLA and a 15 min, 750°C furnace 
anneal. In this picture a high density of small loops have evolved. Comparing the top 
two pictures makes it immediately obvious that the NLA is having a significant effect on 
the defect evolution for this implant and NLA condition. The bottom two pictures from 
left to right are for the samples receiving the NLA plus a 45 min, 750°C furnace anneal 
and the NLA plus a 90 min, 750°C furnace anneal. The pictures show that the loops 



72 

nucleated during the NLA grow into slightly large loops as time increases, but remain 
relatively stable between 45 and 90 minutes. 
5.4.2 532nm NLA 

Figure 5.16 shows the plan-view TEM for the 5 KeV samples processed with the 532 
nm laser as-implanted (top left), after a 750°C, 15 min furnace anneal (top right), a 10 
pulse NLA (center left), a 1000 pulse NLA (bottom left), a 10 pulse NLA plus the 
furnace anneal (center right), and a 1000 pulse NLA plus the furnace anneal (bottom 
right). TEM needs to be redone then the discussion added. Not sure it adds much either. 
Could also add 900C furnace anneal junk here. 900C does not add much. Hall effect 
exists for all, but no SIMS. 

5.5 Conclusions 

The NLA prior to the RTA can reduce the amount the boron diffuses into the sample. 
The NLA prior to the RTA can also reduce the amount of interstitials around to form 
defects during the RTA. Also, the NLA prior to the RTA results in a dramatic change in 
the defects which evolve in the samples. The microscopic change is fairly obvious in the 
TEM: the NLA causes a high density of loops to evolve in samples which may have 
otherwise evolved 3 1 Is or larger loops. Also, although not evident in the samples 
receiving 100 or 1000 pulses prior to the RTA, the SIMS profiles for the samples 
receiving 10 or less pulses prior to the RTA do show the broad diffusion shoulder 
characteristic of high dose boron implants. This implies that much of the surface boron is 
trapped in boron interstitial clusters. Of course, BICs imply deactivation which is one of 
the subjects of the next chapter, Chapter 6. In Chapter 6 the SIMS profiles and defect 
microstructure will be discussed in more detail as the boron diffusion and defect 
structures both influence the activation and mobility of the layer. 



73 




50 100 150 200 250 300 

Depth (nm) 



Figure 5.1 SMS profiles following NLA and 1000°C, 5sec RTA for 5 KeV are shown, 
lei 5 B+ ions/cm 2 samples processed with the 308 nm laser. 



74 



a 

o 

03 

*■» 

• — 

o 




|^Q I I i I I I I I I I I I I I I I I I I I I I I I 

0.1 0.2 0.3 0.4 0.5 



■ ■ I ■ ■ « ■ 
0.6 0.7 



Energy Density (J/cm ) 



Figure 5.2 Sheet Resistance vs. Laser Energy Density following 1000°C, 5sec RTA for 5 
KeV. Iel5 B+ ions/cm 2 samples processed with the 308 nm laser. 



75 




Figure 5.3 TEM following 0.4 J/cm 2 NLA, following 0.6 J/cm 2 NLA, and following the 
RTA (top pictures from left to right), and TEM of samples receiving 0.4, 0.5, or 0.6 J/cm 2 
NLA followed by RTA (bottom pictures from left to right). 



76 



t 

P 



b£ 

•I 

= 

w 

o 
o 

- 
o 

s 



100 



80 












0.1 



0.2 



0.3 



0.4 0.5 



0.6 



Laser Energy Density (J/cm ) 



Figure 5.4 Percentage of loops extending to the surface versus laser energy density for 
1000°C, 5sec RTA of 5 KeV. Iel5 B+ ions/cm 2 samples processed with the 308 nm 
laser. 



77 








0.1 



0.2 0.3 0.4 0.5 



0.6 



Laser Energy Density (J/cm ) 



Figure 5.5 Defect density versus laser energy density for 1000°C, 5sec RTA of 5 KeV. 
lei 5 B+ ions/cm 2 samples processed with the 308 nm laser. 



78 




Depth (A) 



Figure 5.6 SMS of 1 KeV, 10 15 ions/cm2 B following 10 laser pulses, with 1040°C, 5 
sec RTA, and 10 pulse plus 1040°C, 5 sec RTA. 



79 



6000 



a* 




^ 


5000 


Xfl 




S 




pfi 




O 


4000 


w 




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u 







3000 


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. 




. 


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1 10 

# of Laser Pulses 



Figure 5.7 Sheet resistance versus number of laser pulses for 1 KeV, 10 15 /cm2 B for 
samples receiving just the NLA (NLA only) and those processed with 1040°C, 5 sec RTA 
(withRTA). 



80 





10 shots 










" 


' 
















• 




. 


■ 


- ■ ■■ -■ S r 

m 


• 




■ ■ -■ 




Figure 5.8 Plan-view TEM of 1 KeV, lel5/cm 2 boron implanted silicon following (from 
left to right) 10 shots, RTA only, 10 shots plus RTA. 









81 



<r> 



£ 



2 

O 




2000 



Depth (A) 



Figure 5.9 SIMS of 5 KeV, 2el5 B+ ions/cm 2 samples following NLA with the 532 nm 
laser using a 20 ns pulse length at 100 Hz and 1050°C spike anneal compared with the 
sample receiving just the spike anneal. 



82 






a 



= 

+■» 
ft 

CM 



O 

GO 



3000 



2500 



2000 



NLA only 

with 1050°C 
spike anneal 




1 10 100 

# of Laser Pulses 



1000 



Figure 5.10 Sheet resistance versus number of laser pulses of 5 KeV, 2el5 B+ ions/cm 
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz 
and/or 1050°C spike anneal. 



83 




Figure 5.1 1 Plan-view TEM of 5 KeV, 2el5 B+ ions/cm 2 samples following RTA alone, 
one pulse plus RTA, and 10 pulses plus RTA. The NLA is at 0.35 J/cm 2 with the 532 nm 
laser using a 20 ns pulse length at 100 Hz. The RTA is a 1050°C spike anneal. 



84 



**} 



a 




200 300 400 

Depth (A) 



500 



Figure 5.12 SIMS of 500 eV, lel5 B+ ions/cm 2 samples following NLA with the 532 
nm laser using a 20 ns pulse length at 100 Hz and 1050°C spike anneal compared with 
the sample receiving just the spike anneal. 



85 



3000 
^ 2500 

a 

Q 2000 



a 

+■> 

1/5 

-= 
to 



1500 



1000 



500 



NLA only 

with 1050°C 
spike anneal 



I 



1 



± 



± 



1 10 100 

# of Laser Pulses 



1000 



Figure 5.13 Sheet resistance versus number of laser pulses of 500 eV, lei 5 B+ ions/cm 
samples following NLA with the 532 nm laser using a 20 ns pulse length at 100 Hz 
and/or 1050°C spike anneal. 



86 




Figure 5.14 Plan-view TEM of the 500 eV, lel5 B+/cm 2 sample annealed with a 1050°C 
spike anneal. 



87 











- y 



3 » *.- 



• .*» 



M «m •'•• 



Figure 5.15 Plan-view TEM of 5 KeV, lei 5 B+ ions/cm 2 samples after 750°C furnace 
anneal (top left), NLA plus 750°C, 15 min furnace anneal (top right), NLA plus 750°C, 
45 min furnace anneal (bottom left), and NLA plus 750°C, 90 min furnace anneal 
(bottom right). The NLA is with the 308 nm laser using one 15 ns pulse at 0.6 J/cm 2 . 



gg 






2500 
U5 2000 

a 

B 
O 

^ 1500 

I 
3 1000 

I 



-= 



500 - 



B 




_ 


■ 


— •— NLA only 
-» - plus FA 


- 






- 


1 T- 







1 10 100 

# of Laser Pulses 



1000 



Figure 5.16 Sheet resistance for the 5 KeV, 2el5/cm 2 samples receiving the 532 nm 
NLA and/or the 750°C furnace anneal. 



CHAPTER 6 
EFFECTS OF NLA ON MOBILITY AND ACTIVATION 

6.1 Introduction 

The focus of this work is to explain the effects of NLA on silicon implanted with a 

high dose (>lel5/cm 2 ) of boron. This requires understanding the effect of the NLA on 

the electrical properties of the boron-implanted layer. It also requires understanding how 

the electrical and physical properties of the layer interact. In this chapter the mobility and 

activation data for the experiments presented in chapters 3 through 5 will be presented 

and discussed. The mobility, hole density, and sheet resistance are all measured using the 

Hall effect and a hall factor of 0.7 as described in Chapter 1. The results are presented 

and compared to the plan-view TEM and SIMS results from Chapters 3 through 5. SIMS 

profiles along with Hall measurements allow determination of the actual amount of boron 

which is inactive in the annealed layer. Analyzing SIMS profiles, and the defect 

microstructure, along with knowing how much inactive boron exists can help determine 

if boron clustering is occurring. Knowing the type of defects in the system and the 

distribution of the defects is essential to predicting the electrical properties of the layer. 

First, the various factors which affect the activation and deactivation are discussed. 

Then, the mobility and sheet resistance data are examined. Finally, the effect of the loops 

on the mobility and activation is shown and discussed. 



89 



90 

6.2 Experimental Results 
6.2.1 The 308 nm Experiments 

Samples implanted with boron at 5 KeV, 2el5 ions/cm or 1 KeV, lei 5 ions/cm 
are annealed using a 308 nm NLA at a constant energy density of 0.6 J/cm . The pulse 
frequency is set at 10 Hz and the pulse length at 15 ns. To further understand the effects 
of NLA on the boron implanted samples, some of the samples receiving the NLA and a 
sample receiving no NLA are annealed with a 1040°C, 5 sec RTA. 

Hall effect measurements can be made on all of the samples after the RTA. However, 
for the 5 KeV samples receiving one and ten laser pulses Hall effect measurements 
cannot be made. The heavy damage remaining from the implant is believed to cause 
significant error in the measurements. For example, if ohmic contacts can be made to the 
material, the currents measured are found to vary by more than 10% between the contacts 
for a fixed voltage. This nonuniformity in resistance between the contacts makes it 
impossible to obtain any useful information from the Hall measurements. For these 
samples the mobility and the hole densities are set to zero. Figure 6. 1 shows plots of the 
hole mobility (top) and the hole density (bottom) as a function of the number of laser 
pulses for the 5 KeV samples. These plots show the NLA has no measurable effects on 
the 5 KeV samples until 100 pulses. After 100 pulses with the NLA, the mobility and the 
hole density both increase. However, when followed with an RTA, the mobility 
decreases slightly from 43 to 40 cm 2 /V-s while the hole density drops by nearly 75%. 
Figure 6.2 shows the percent activation as a function of laser pulses for the 5 KeV 
samples. To determine the activation, the active dose (the hole density) is divided by the 
implant dose of 2el5 ions/cm 2 . This dose is also the dose calculated from the SIMS 
profiles shown in Chapter 3. 



91 

Figure 6.3 shows plots of the hole mobility (top) and the hole density (bottom) as a 
function of the number of laser pulses for the 1 KeV samples. For the 1 KeV implants, 
the 308 nm NLA alone causes the mobility and the hole density to increase as the number 
of laser pulses increases. However, post-processing with the RTA causes an increase in 
the mobility and a decrease in the hole density. The plots for the activation are shown in 
Figure 6.4. The top plot is the hole density divided by the implant dose. The bottom plot 
is for the hole density divided by the actual implanted dose of 7.4el4 ions/cm . The dose 
is calculated by integrating the SIMS profiles of Chapter 3. According to the SIMS 
profiles, no dose loss is found to occur during the NLA or RTA. This means the same 
dose is used to determine the activation for all annealing conditions. Dose loss does 
occur during the boron implantation step. The dose loss during the implant is found to be 
26% of the implanted dose. Using the dose of the implant (lel5/cm 2 ) will tell you the 
efficiency of activation at that implant dose. However, the actual dose which makes it 
into the sample must be used to accurately describe the actual electrical activation in the 
implanted layer. 
6.2.2 The 532 nm Experiments 

This next set of experiments uses the 532 nm laser for the NLA. For these 
experiments, a constant energy density of 0.35 J/cm 2 , a pulse frequency of 100 Hz, and a 
pulse length of 20 ns, is used. The implant conditions are 5 KeV, 2el5 B+ ions/cm2 and 
500 eV, 2el5 B+ ions/cm2. The number of pulses is varied from one to 1000. Some of 
the samples receiving the NLA and some which do not receive the NLA are post- 
processed with a 1050°C spike anneal. The plots are prepared to show how the NLA and 
post-processing affect the mobility and hole density. 



92 

Figure 6.5 shows the plots of the mobility and hole density versus number of laser 
pulses for the 5 KeV implants. Figure 6.6 shows a plot of the percent activation versus 
number of laser pulses for the 5 KeV implants. For this plot, the percent activation is 
determined by dividing the hole density by the implant dose of 2el5 ions/cm which is 
also the dose calculated from SIMS profiles. As shown, the mobility and activation 
increase as the number of laser pulses increases. Post-processing with the RTA, 
however, causes deactivation and for the most part an increase in the hole mobility. 

Figure 6.7 shows the plots of the mobility and hole density versus number of laser 
pulses for the 500 eV implants. The plots for the activation are shown in Figure 6.8. The 
top plot is the hole density divided by the implant dose of lei 5 ions/cm 2 , and the bottom 
plot is for the hole density divided by the actual implanted dose calculated from the SIMS 
profiles. The as-implanted dose is found to be 7.0el4/cm 2 . Once again, dose loss occurs 
during the implant. However, for this implant dose loss also occurs during the 
subsequent annealing steps. 

Figure 6.9 shows the amount of dose lost during the NLA and RTA steps. The top 
plot shows the change in dose during the NLA and the NLA followed by the RTA. The 
bottom plot shows the percentage of dose lost during the RTA. These quantities will 
become more important when analyzing the effect of the NLA and RTA on boron 
activation. 

6.3 Discussion 
6.3.1 Overview 

For the percent activation plots, dividing the hole density by the implant dose shows 
the negative effect of the dose loss during implantation on the total boron activation. 
However, dividing the hole density by the actual dose that makes it into the sample 



93 

allows for the calculation of the actual amount of inactive boron left after the anneals. 
This quantity is more relevant to understanding the electrical characteristics of the 
implanted layer. 

All of the plots show the NLA alone causes the mobility to increase and the activation 
to increase as the number of laser pulses increases. Both are positive effects that result in 
lower sheet resistances for the individual cases. However, when the results from all of 
the experiments are plotted together versus sheet resistance it becomes apparent that the 
hole density is dominating the change in sheet resistance. Figure 6. 10 shows the plots for 
the hole density and hole mobility versus sheet resistance. The plot for the hole density 
versus sheet resistance shows how increasing the hole density decreases the sheet 
resistance. However, the plot for the mobility versus sheet resistance shows no trend. 
Thus, the changes in sheet resistance as a whole appears to be dominated by the change 
in the hole density (active boron dose) and not by the mobility. Lets investigate whether 
this change as a whole can be explained by the defects visible in plan-view TEM 
presented in Chapters 3 and 4. 

Plots of the mobility versus the loop dose and interstitial dose are shown in Figure 
6.1 1. Plots of the percent activation versus the loop density and interstitial density are 
shown in Figure 6.12. The mobility and the activation show no strong trends when 
compared to the interstitial densities and loop densities observed using TEM. This is 
surprising, since it is generally thought that more defects would mean more scattering 
sites, and more scattering sites would cause a decrease in the mobility. 
6.3.2 Boron Activation. Deactivation, and Precipitation 

So far, the only obvious trend is that the sheet resistance is dominated by the changes 
in activation. This section will further investigate the causes of the boron activation and 



94 

deactivation. Figures 6.1 through 6.8 show that in general, the RTA after the NLA 
decreases the hole density. A decrease in the hole density means that boron deactivation 
is occurring. Comparing the bottom plot in Figure 6.8 with Figure 6.6 shows that only 
35% of the boron is being activated during the NLA of the 500 eV samples versus 95% 
activation in the 5 KeV samples. There are only three cases where the RTA after the 
NLA does not cause boron deactivation. These are for three of the 500 eV samples. 
These samples are the ones given one, ten, or 100 pulses prior to the RTA. 

Plan-view TEM of the 5 KeV as well as the 500 eV samples shows that no defects 
exist in the 5 KeV samples after 1000 pulses or in the 500 eV samples after 10, 100 and 
1000 pulses (Chapter 4). Also, SIMS results show that boron diffusion into the samples 
during the RTA occurs only slightly for the 5 KeV and 500 eV samples that receive a 100 
or 1000 pulse NLA prior to the RTA (Chapter 4). What the results for the 5 KeV and 500 
eV samples imply is that interstitials are not available after the 100 and 1000 pulse NLA 
to significantly contribute to boron diffusion (TED) or extended defect formation. 

In the 500 eV samples, if most of the interstitials were gone then this would mean that 
no interstitials should be available to form boron interstitial clusters. This raises a 
question on why the boron is not continuing to activate as the number of laser pulses 
increases. With so few interstitials around, a boron rich region, and a high temperature 
anneal, a possible explanation might be boron precipitation. The 500 eV implant results 
in a significantly higher boron concentration of 2 to 3e21 B+ ions/cm 3 versus 7e20 B+ 
ions/cm 3 for the 5 KeV implants. During one pulse interstitial clusters form and boron 
activates. During the next nine pulses, the boron begins to diffuse and the interstitial 
clusters grow. Somewhere between 10 and 100 pulses, the interstitial clusters have 



95 

dissolved or have been consumed by the surface. The lack of interstitials available, and 
the high boron concentration suggests that if any boron interstitial clusters are forming 
they would be predominately boron after 100 and 1000 pulses. 

This does seems to suggest the possibility that these boron clusters are actually boron 
precipitates, which form during 10 to 100 pulses with the NLA. These precipitates would 
be sub-microscopic and evenly distributed in the layer. This distribution could produce a 
uniform strain making them undetectable during TEM analysis. 

Is boron precipitation realistic? Recall from the SIMS that the boron peak 
concentration in the 500 eV samples is 2 to 3e21 B+ ions/cm 3 while it is only 7e20 B+ 
ions/cm 2 in the 5 KeV samples and le21 B+ ions/cm 3 in the 1 KeV samples. Since the 
solid solubility limit is around 2e20/cm 3 for the temperatures reached during the NLA, 
this concentration is certainly high enough to result in boron precipitation in the 500 eV 
samples. 

However, precipitation is unlikely the cause since the following scenario during the 
RTA would have to occur: During the RTA, the precipitates would have to dissolve 
which would supply boron to the layer and not interstitials. Thus resulting in an increase 
in boron activation without TED. Unfortunately, a 1040°C, 5 sec RTA is not likely to 
supply enough energy to break up a BIC let alone dissolve a precipitate. Also, the 5 KeV 
boron concentration is also high enough (2e20/cm 3 at the surface and 7e20/cm 3 at its 
peak) that boron precipitation would occur. Since nearly 100% of the 5 KeV implant can 
be activated it is even more unlikely that precipitates formed during the NLA of either 
set. So, the dissolution of boron precipitates is not likely to be a reasonable explanation 
for the boron activation during the RTA 



96 

6.3.3 Boron Activation. Deactivation. Tnterstitials . and Diffusion 

Since precipitation is probably not the answer, the amount of interstitials available and 
the boron diffusion occurring may help explain the deactivation and activation in the 500 
eV samples. As to the question on why the boron does not continue to activate in the 500 
eV samples compared to the 5 KeV samples, this can be explained by considering the 
number of interstitials available in the system and the amount of boron diffusion. In 
samples where deactivation is occurring there must still be interstitials around with the 
amount decreasing as the number of laser pulses increases. The decrease in interstitials 
available is evident due to the decrease in diffusion seen in the SIMS as the number of 
laser pulses increases prior to the RTA. The decrease in interstitials available also 
decreases the amount of boron deactivation when the RTA is given to the samples. The 
decrease in deactivation is shown in Figure 6.6 where one pulse plus the RTA causes 
80% deactivation and 1000 pulses prior to the RTA only results in 15% deactivation. 
This decrease in deactivation is due to the decrease in the number of interstitials available 
after the NLA. The deactivated boron in all cases where no loops are present is most 
likely due to the formation of BICs during the RTA. 

In the 500 eV samples eventually the amount of interstitials is low enough that BICs 
cannot be formed during the RTA. The lack of interstitials available to later form BICs 
also means there are no interstitials around for sufficient boron diffusion. With little 
increase in boron diffusion between 10 to 100 and 100 to 1000 pulses, the amount of 
boron activated during the NLA reaches a plateau between 10 to 100 pulses. When the 
RTA is applied to these samples, which have fewer interstitials, fewer if any BICs form. 

The activation resulting is due to the boron diffusion during the RTA. Recall in 
Figure 6.9 that significant dose loss occurs during the RTA. This dose loss requires a 



97 

significant amount of boron diffusion out of the peak region and into the oxide and 
silicon/oxide interface. During this diffusion, the boron becomes substitutional by 
interaction with vacancies or the interstitial kickout. The free interstitial can then pair 
with another boron causing diffusion and more activation. Anyway, boron in the 
presence of a few interstitials results in some boron diffusion which causes more boron 
activation than BIC formation. 

So, if so few interstitials are available prior to the RTA of these 500 eV samples, what 
is the reason for so much diffusion which results in the dose loss and boron activation? 
This brings us back to the idea of boron enhanced diffusion (BED). A phenomena 
believed to happen in samples implanted with high doses of boron (5el4-lel5/cm2) 
[Aga98, Aga99]. BED requires the formation of a silicon boride phase, SiB4. During 
the formation of the silicon boride the excess silicon is injected into the nearby region as 
silicon interstitials. These interstitials lead to a type of TED which is called BED. If this 
silicon boride phase forms during the NLA then the excess interstitials would cause BED 
during the NLA and increased diffusion during the RTA due to the extra interstitials. 
Since samples receiving one pulse prior to the RTA do in general diffuse more than the 
sample receiving just the RTA there is a possibility that SiB4 is forming resulting in 
BED. However, all of the diffusion seen during the NLA alone can be explained by the 
normal TED expected as defined by the boron-interstitial pair diffusion from Chapter 1. 
6.3.4 Mobility and Sheet Resistance 

Characterization of actual semiconductor devices requires knowledge of the mobility, 
dopant density, sheet resistance and the chemical and electrical junction depth. Plots of 
mobility versus concentration and sheet resistance versus junction depth are often 
presented and compared to theory. The mobility is generally plotted as a function of the 



98 

carrier concentration when being discussed in papers [Thu81, Kla90, Kla92, Li79]. 
Therefore the results for the mobility versus concentration of this work will also be 
presented. Figure 6.13 shows how the mobility varies as a function of hole concentration 
for the 308 nm and 532 run experiments. Comparison to previously published data shows 
that the values are reasonable [Thu81, Lin81]. In this figure the hole concentration is 
determined by using the junction depth measured from SIMS at a boron concentration of 
lei 8 ion/cm . Using this chemical junction depth along with the hole density predicted 
using Hall effect is really not valid for the gaussian-like boron profiles produced by 
implantation, especially when the entire profile is not activated. Instead, the active boron 
profiles must be known and those profiles integrated to determine at what depth the given 
Hall density given could be obtained. Using this approach, the junction depth would 
most likely decrease and the hole concentration increase. Once again, describing a box- 
like profile with a concentration over a given depth is more applicable. 

Another plot which is very common in industry is the sheet resistance versus junction 
depth plot. Figure 6.13 shows plots of the sheet resistance obtained as a function of 
junction depth. The top plot shows the results from all of the experiments. The bottom 
plot shows the benefit of NLA versus using the convention RTA. Typically the goal is to 
continually try to make shallower layers with lower resistivities and produce data points 
that appear in the southwest corner of the sheet resistance versus Xj plot. Note that using 
the NLA allows for the creation of shallower layers with lower sheet resistances than 
conventional annealing techniques. 
6.3.5 Mobility. Activation, and Loops 

It has been shown that the NLA alone can cause the boron activation and mobility to 
increase in the samples with the benefits of increasing the number of laser pulses 



99 

diminishing as the number of laser pulses increases. Also, the mobility and activation are 
not to any great extent affected by the density of visible defects or by the density of the 
interstitials in those defects. So it may appear that the mobility and activation are not 
affected by the loops. However, recall the TEM microstructure shown in Chapter 3 and 4 
after the NLA. The NLA caused the nucleation of a high density of tiny defects which 
have been and will be called loops in order to simplify the discussion. 

Logically, the presence of this large number of small loops must be affecting the 
electrical properties of the layer. The loops act as scattering sites for holes (or electrons). 
Increasing the number of scattering sites, decreases the average time between collisions 
for the hole which decreases the hole mobility. Scattering from a loop can be due to the 
strain fields in the silicon due to the presence of the extra atoms. The scattering can also 
be attributed to an effective charge due to dangling bonds at the edges of the loops. This 
type of scattering would be similar to ionized impurity scattering. 

If it is not the loop density or the interstitial density alone then perhaps the influence 
of the size of the loop on the mobility and activation needs to be investigated. Figure 
6.15 shows the plots for the hole density and hole mobility versus the average radius of 
the loops. The average radius calculated using the following equation: 

CbLoops = rc* R • n a ■ dLoops (6.1) 

where Ci,Loops is the concentration of interstitials in the loops, 7tR 2 is the fractional area of 
the loops, ria is the atomic density of the <1 1 1> plane (1.5el5/cm 2 ), and dLoops is the 
density of the loops. As you can see both plots show strong trends. As the average size 
of the loops increases, the hole density decreases and the hole mobility increases. Having 
the mobility drop as the size drops implies that the smaller loops are more effective at 



100 

causing hole scattering than the larger loops. A possible explanation is that the small 
loops are causing scattering similar to the scattering caused by the neutral impurities in 
the layer. Also, the high activation in the presence of the small loops suggests that they 
are not very effective at gettering or trapping boron. If these loops were effective at 
capturing boron then the hole density would be much lower. Also, note that as the 
average size of the loops increases the boron activation decreases. This suggests that the 
larger loops are quite effective at trapping and deactivating boron. 

6.4 Conclusions 

The mobility and activation data for various anneals with the NLA, the RTA, and the 
NLA followed by the RTA have been shown. The NLA is found to increase activation 
and mobility as the number of laser pulses is increased. This makes it possible to 
produce shallower junctions with lower sheet resistances than conventional processing 
techniques. Also, the mobility and activation of the layers as a whole are found to vary 
significantly as a function of the average number of interstitials in the loops and not as a 
function of the total number of interstitials or loops observed in TEM. 

Now that a conclusion about the effect of the loops on the mobility and activation has 
been reached, an effort will be made to further quantify and model the results. Using the 
theory and a model developed over time by Li, Lin, and Linares [Li79, Lin81] for 
analyzing the mobility of holes in p-type silicon, a reasonable fit to the data presented can 
be made as long as the samples contain large loops or no loops. The model becomes less 
accurate as the average number of interstitials in the loops decreases. In Chapter 7 a 
mobility model will be presented which extends Li's model to also include the scattering 
from the loops. Using this improved mobility model along with FLOOPS (Florida Object 



101 



Oriented Process Simulator), the average mobility and sheet resistance of the implanted 
layer after various anneal steps can be found. 



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Figure 6.1 The Hall mobility vs. laser energy density is shown following 1040°C, 5 sec 
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103 






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Figure 6.2 Plot of the percent activation vs. laser energy density following 1040°C, 5 sec 
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(with RTA). Top picture represents the active dose divided by the dose of the implant, 
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Hz and/or 1050°C spike anneal. 



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Figure 6.6 Percent activation versus number of laser pulses of 5 KeV, 2el5 B+ ions/cm 
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ions/cm 



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Figure 6.7 Mobility and hole density versus number of laser pulses of 500 eV, lel5 B+ 
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Hz and/or 1050°C spike anneal. 



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from SIMS following each anneal step. The bottom plot shows the percent of dose which 
is lost during the RTA. 



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Figure 6. 13 Hole mobility versus hole concentration for all processing conditions. The 
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Figure 6.14 Sheet resistance as a function of junction depth for all processes (top) and 
NLA alone compared with the conventional RTA (bottom). Xj is measured at a boron 
concentration of lxl0 18 /cm 3 . The arrows show the benefit of using NLA over 
conventional processing anneals. 



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♦ 






w 






A 






i 


40 




"* 




-| 


A 










■ 


1 


30 








- 












■ 








■ 


■ IKeV 


308nm 


■ 


© 


20 






* 5KeV 


308nm 


— 


= 


10 






♦ 5KeV 


532nm 


■ 








1 ■ 








200 


400 




600 








Average I 


ladius, R 


(A) 





Figure 6.15 Plots of the hole density and hole mobility are shown versus the average 
radius of the loops. As you can see both plots show strong trends. As the average radius 
of the loops increases, the hole density decreases and the hole mobility increases. 



CHAPTER 7 
MODELING THE MOBILITY 

7.1 Introduction 

Due to the complexity of integrated circuit processing, it has become increasingly 
more difficult and time consuming to develop new processes. The use of process 
simulators such as FLOOPS (Florida's Object Oriented Process Simulator) can help 
improve and expedite the development of new processes. Using experimental results to 
improve and create models for process simulation is very useful in new technology 
development. Knowing the mobility and activation as a result of an implant followed by 
anneal steps allows the calculation of the sheet resistance of the layer along with 
information on the effects of the defects in the region on device performance. If for 
example FLOOPS is used to predict the boron activation and defect clusters as well as 
their distribution, this information can be used in combination with an accurate mobility 
model to predict the resistivity of a boron implanted layer after processing. The implant 
conditions and anneal steps can then be altered until the desired results are obtained. 

In the preceding chapters, emphasis is placed on the experimental results for nonmelt 
laser annealing of boron-implanted silicon. In Chapter 6, the influence of the physical 
properties of the device on the electrical properties is examined. Notably, the mobility is 
determined to be influenced by the average radius of the loops. Although a few mobility 
models exist for silicon none of these models consider the effect of the damage evolving 
during the anneal [Ben83, Ben85, Ben86, Kla90, Kla92, Li79, Lin81]. In this chapter a 
theoretical mobility model created and improved upon over time by Li and Linares [Li79. 

117 



118 

Lin8 1] is examined and compared to the data presented in Chapter 6. The model though 
developed for lower doping ranges is shown to accurately predict the mobility when the 
number of defects present is small compared to the amount of active boron. However, 
the mobility calculated by the model predicts higher mobilities than shown in 
experiments when the defect density is high and the size of those defects small. 
Therefore, the model is further improved by adding the effect of the defects on the 
mobility. By making the neutral impurity scattering dependent on the interstitial and 
defect densities which can be quantified from TEM, a reasonable fit to the data can be 
found. 

7.2 Li's and Linares' Mobility Model 
Linares and Li have created a model for analyzing the hole mobility in p-type silicon 
which considers the effects of lattice, ionized impurity, and neutral impurity scattering 
[Lin81]. They have also taken into account the effects of hole-hole scattering and the 
nonparabolic nature of the valence band. Their model has been compared to data for hole 
densities varying from 10 14 to 10 18 holes/cm 3 . The model is based on the theoretical 
model originally developed by Li [Li79]. The model derives the number of neutral and 
ionized impurities for a particular boron concentration. The combined mobility for the 
lattice and ionized impurity scattering, uli, is found using the mixed-scattering formula 
[Deb54]. The total hole mobility is found by using Mathiesson's Rules to combine uli 
with the neutral impurity mobility, ^ N . Using Mathiesson's Rule here should not add 
significant error to the total hole mobility since u*i does not affect contributions from uj 
(ionized impurity mobility) or p L (lattice mobility). It has been implemented in FLOOPS 
to handle a variable boron concentration as an input. The result is a positional dependent 
mobility related to the active and neutral concentrations of boron. Therefore, using the 



119 

SIMS profiles presented in Chapters 3 and 4 and FLOOPS the model can be used to 
predict the average mobility and sheet resistance after each anneal step. The results are 
presented in Figures 7.1 and 7.2. Recalling the defect microstructure in each sample, it is 
shown that the model accurately predicts the results for the mobility and sheet resistance 
for samples known or expected to contain only a few defects or large loops. 

As shown, the model only appears to fail when the defects in the sample are small and 
numerous. Therefore, in order to make the model more accurate for the more heavily 
doped boron implanted silicon presented in this work, it is also necessary to take into 
account the scattering due to the defects remaining in the sample after the anneal steps 
are completed. The defects may be loops, 311s, sub-microscopic interstitial clusters 
(SMICs), and/or boron -interstitial clusters (BICs). Knowing more information about the 
distribution of the BICs would most likely further improve the model. In Chapter 6 the 
mobility is shown to be dependent on the average radius of the loops. If the loops are 
considered to be neutral it seems to make sense to see if increasing the number of neutrals 
will lead to a better fit to the data. 

7.3 The Improved Mobility Model 
The influence of the defects on the mobility and the carrier activation is related to the 
distribution and size of the defects in the active layer. These defects disrupt the 
periodicity of the lattice which decreases the mobility. The high density of defects 
formed after the NLA also results in a fairly uniform distribution of the defects across the 
layer. This type of distribution itself will decrease the mobility more than the large loops 
because the distance between the scattering sites has been dramatically reduced compared 
to the defects which would typically evolve. Since these defects have been shown to 
evolve into loops, they will once again from hereafter be referred to simply as loops. 



120 



The reduction in mobility by the loops comes from its ability to scatter a carrier 
which is traveling through the lattice. One of the properties of a loop which can cause 
scattering is the strain resulting from its presence in the lattice. Since a loop only causes 
strain in the lattice around its circumference, the amount of scattering that a loop can do 
must be related to its circumference of 2*R where R is the radius of the loop. By 
analyzing plan-view TEM images, the average size of the loops can be obtained. 

The following method is thus evolved to estimate the scattering cross section of the 
loop. The fraction of the area of the loop which causes the scattering is described by 2tcR 
times L, where L is the width of the strain field which extends around the perimeter of the 
loop. The area of the whole loop is t:R 2 . Dividing 2rcRL by rcR 2 produces the fractional 
area of the loops which are participating in scattering. Multiplying the number of 
interstitials/cm 2 trapped in loops by the fractional area of the loop which participates in 
scattering gives an estimate of the number of neutral interstitials per cm 2 which is 
contributing to the scattering. Fitting this dose to a distribution similar to that of the 
boron implant produces a concentration of neutrals which can be added to the number of 
neutrals used in the mobility model. The model is developed as follows: 

Dn,Loo P s = Dloo P s*2tcRL (7-D 

where 

D i,Loops = *R 2 * V D Loops < 7 ' 2 ) 

is solved for R which is then substituted into Equation 7.2. R is the average radius of the 
loops, n a is the density of atoms in the <1 1 1> plane of 1.5el5/cm 2 , L is the width of the 
scattering region, D Loops is the density of loops observed in the TEM, D i^ps is the 



121 



density of interstitials trapped in the loops observed in TEM, and D N , Loops is the density 
of neutrals participating in the scattering from the loops. This density of neutrals is then 
converted into a concentration versus depth profile with a peak near the projected range 
of the implant. These neutrals are finally added to the number of neutrals used in Li's 
model to predict the mobility. The results for simulations of the mobility and sheet 
resistances after the NLA, after the RTA, and after the NLA followed by the are 
presented in Figures 7.3 through 7.6 for the 5 KeV and 1 KeV data. An L of 16 A is 
used for all of the data. A full description of the model along with the FLOOPs files can 
be found in Appendix B. 

As shown in all of the figures, the improved model provided a nice fit to all of the 
samples processed with the NLA alone. However, in Figure 1, the mobility is 
underestimated in the 5 KeV samples for samples receiving no laser pulses, one laser 
pulse, or 10 laser pulses prior to the RTA. Also, the mobility is overestimated in the 1 
KeV sample which received only the RTA(Figure 7.5). Although this variation is within 
10% of the experimental result value. 

Since the model requires input from SMS and TEM defect quantification, the error in 
the data can cause the type of variations seen in the 1 KeV plot. The 5 KeV plot suggests 
that further investigation of the model is required. Since the model underestimates the 
mobility, it is believed that the error comes from the interpretation of the SIMS data. All 
of the former SIMS plots showed some dose loss in the sample following the RTA. The 
dose loss from the sample is shown to decrease as the number of laser pulses prior to the 
RTA increase. If some dose loss occurred in the 5 KeV samples, the total amount of 
boron would be reduced. The number of neutral boron is determined from the total boron 



122 

dose. The total number of neutrals is found from the number of neutral boron and the 
loops. Therefore, any extra boron would cause the number of neutrals to be 
overestimated. If the dose of the boron is adjusted for -7% dose loss in the samples 
following the RTA the simulation can be made to fit the experimental results. 

Of course, this adjustment brings us to an interesting point. The results are highly 
dependent on the SIMS profiles, especially the total dose in those profiles. Using the 
model on simulated implanted profiles that do not account for dose loss will add 
significant error to the results. 

Also, the mobility is found to be dependent on both the neutral impurity scattering and 
ionized impurity scattering when the loop density is sufficiently high (such as after 
NLA). Typically, dislocation loops may be thought to produce mid-gap states in the band 
gap. If these states existed at mid-gap, then their effect o mobility should disappear as 
the temperature is decreased and ionized impurity scattering would dominate Hall 
mobility versus temperature measurements, however show that from 300K down to 70K 
there is no change in the mobility. This suggests that the scattering from the loops is not 
due to a mid-gap trap level produced by the loops. The scattering must therefore be 
dominated by scattering from the strain field around the loop. This justifies the 
assumption of increased neutral scattering due to the presence of loops used in this 
model. 

7.4 Conclusions 

A simple model for the mobility has been presented which results in fairly accurate 
fits to samples processed with the NLA. The model suggests that the degradation seen in 
the mobility after the NLA can be directly related to the change in microstructure 
following the NLA. This change in microstructure results in an increase in the number of 



123 

neutral scattering sites which is proportional to the circumference of the loops. The 
model shown happens to fit the data for the current experiments fairly well. However, 
the model of course is quite simple as far a mobility models go. The terms are straight 
forward and require user input from physical analysis. A more detailed model would be 
based on many more experimental results over a wider range of conditions. This model 
would also add the effects of BICs and possibly precipitates on the mobility. Regardless 
of what this model does not contain, it does show the dependence of the mobility on 
loops. In case you missed it, the high concentrations of small loops increase the carrier 
scattering and decrease the mobility. 



124 



80 



i 



a 

a 

o 



w 




Theory after NLA 
Theory after RTA 



1 10 100 

# of Laser Pulses 



1000 



Figure 7.1 This plot compares the theoretical results to the experimental results for the 
hole mobility versus number of laser pulses after 532 run NLA. The 5 KeV, 2el5/cm2 
samples are used. 



125 



tt 



<h 



a 

l 

I 

= 



80 
70 
60 
50 
40 
30 
20 
10 



-•- after NLA 
-» -after RTA 
— *— Theory after NLA 
— •—Theory after RTA 




# of Laser Pulses 



Figure 7.2 This plot compares the theoretical results with the experimental results for the 
hole mobility versus number of laser pulses. The 1 KeV, Iel5/cm2 sample results shown 
here are processed with the 308 nm laser. 





126 




80 r 












E 3 






70fc^ 






■ 


■>. 




i 


60 4 


t N — 




c* 




^»»w_ ^™ 




a 




^N^__ "^ - 






50 






1 


40 












pfi 






o 


30 


^^^^r 








-•-after NLA 




20 


— / 


-»- after RTA 


■ 


o 




M 


Simulation after NLA 


> 


10 


'- / 


—♦—Simulation after RTA 


t 


y _j 


. 1 




i 10 100 1000 




# of Laser Pulses 


Figure 7 3 The hole mobility versus the number of laser pulses is shown for the 5 KeV, 
Sm2 samples processed with the 532nm laser. The simulation used here mcluded 


the dependence c 


if the number of neut 


rals on the size ot tne loop. 





127 



9 

a 

- 

o 

qj 

= 

CM 

+* 
QJ 

GO 



1000 



800 






-♦-after NLA 

-■ after RTA 

— *- Simulation after NLA 

—•—Simulation after RTA 








1 10 100 

# of Laser Pulses 



1000 



Figure 7 4 The sheet resistance versus the number of laser pulses is shown for the 5 
KeV, 2el5/cm2 samples processed with the 532nm laser. The simulation used here 
included the dependence of the number of neutrals on the size of the loop. 



128 




40 
30 
20 



-•-after NLA 
-» -after RTA 

Simulation after NLA 

— ♦— Simulation after RTA 




# of Laser Pulses 



Figure 7.5 The mobility versus the number of laser pulses is shown for the 1 KeV, 
Iel5/cm2 samples processed with the 308nm laser. The simulation used here included 
the dependence of the number of neutrals on the size of the loop. 



129 



2000 






1500 - 



9 

s 

g 

d 

.22 



** 500 - 



1000 - 





after NLA 
after RTA 
Simulation after NLA 
Simulation after RTA 







10 



# of Laser Pulses 



w™,«. 7 6 The sheet resistance versus the number of laser pulses is shown for the 1 
ffiS& with the 308nm laser. The simulation used here 
mcluded the Jdependence of the number of neutrals on the size of the loop. 



CHAPTER 8 
SUMMARY, CONCLUSIONS, AND FUTURE WORK 

8.1 Summary 

In this dissertation, the effects of nonmelt laser annealing on silicon heavily doped 
with boron are investigated and analyzed. In FLOOPS, a model using the one- 
dimensional heat flow equation along with surface radiation is implemented to show the 
temperature distribution in the wafer during the NLA and during the cooldown. The 
boron implanted silicon is investigated after multiple pulses with the NLA. The results 
are compared to samples receiving the more conventional RTA. To further understand 
how the NLA affects the electrical and structural properties of the implanted layer, the 
effects of post-processing on the samples receiving the NLA are also investigated. 
Finally, a model for the hole mobility is also implemented in FLOOPS. 

In Chapter 1, the motivation and objectives of this work are presented. The ion 
implantation process as well as the various electrical and structural analysis techniques 
related to this work are reviewed. The physical processes of activation, and annealing, 
are discussed. A discussion of the RTA which is currently used for dopant activation in 
silicon is presented along with an overview of the laser thermal annealing. 

In Chapter 2, the laser-solid interactions are discussed. A model for the temperature 
distribution in silicon during the NLA is shown. This model also includes the effect of 
surface radiation during the NLA and cooldown which is generally neglected in thermal 
estimations. Modeling the temperature allows determination of the total thermal budget 
observed in the annealed layer. Understanding the temperature distribution in relation to 

130 



131 

the boron and damage profiles aids in understanding the defect evolution and boron 
diffusion during the NLA. Since the temperature distribution is related to the absorption 
depth of the laser, it is shown that it is important to make sure the implanted region lies 
within this depth. Of course, this is on the assumption that the desire is to have the entire 
implanted layer fully annealed. To further investigate the effect of the absorption depth 
on the samples, the NLA studies are performed with the 308 nm laser and the 532 nm 
laser which have absorption depths of -70 A and 5000 to 10000 A respectively. These 
absorption depths are for optical measurements made on crystalline silicon. 

This brings us to Chapters 3 and 4 which show the results of the 308 nm and 532 nm 
laser anneals on the boron distribution and defect evolution. For 5 KeV implants no 
diffusion is observed in the boron profiles during the NLA with either laser. For the 
shallower 1 KeV and 500 eV implantes, the NLA results in slight diffusion of the boron 
profiles during the NLA. Despite the lack of boron diffusion, the NLA alone is also 
shown to decrease the sheet resistance in the layers as the number of laser pulses is 
increased. Finally, the NLA alone is shown to cause the nucleation of a high-density of 
small defects which are visible in TEM. 

Chapter 5 uses a longer anneal than the NLA to post-process the samples which 
receive the NLA. This longer anneal shows that the defects observed after the NLA 
evolve into a high density of small loops. These loops are smaller and higher in density 
than in the samples receiving just the RTA or furnace anneal. The NLA is even shown to 
cause loops to form in samples which may have otherwise evolved a uniform distribution 
of larger loops and 311s. The post-processing also shows that for the lower implant 
energies the NLA dramatically if not completely reduces the boron diffusion into the 



132 

wafer. This lack of diffusion implies that the interstitials available for TED are 
drastically reduced as the number of laser pulses increases. The diffusion, interstitial, and 
defect information gained here aids in the understanding of the electrical properties 
measured in the layers. This brings us to an investigation of the effects of the NLA on 
activation and mobility which is done in Chapter 6. 

In Chapter 6, the activation and mobility are shown to increase as the number of laser 
pulses during the NLA increases. The activation in the samples with the NLA is also 
shown to approach 100% in some samples where the conventional RTA only typically 
results in 10 to 20% activation in the samples. The NLA is in general shown to reduce 
the mobility in the samples which receive the NLA prior to the RTA. It is shown that the 
reduction in mobility is not dominated by the individual changes in the interstitials 
trapped in the loops or the number of loops visible in TEM. However, this mobility 
reduction is shown to be strongly dependent on the average size, or average radius, of the 
loops. 

The dependence of the mobility on the average radius of the loop is related to the 
scattering by the circumference of the loops. This scattering is incorporated into an 
existing mobility model. This model shows that the scattering from loops and thus the 
mobility reduction can be accounted for by simply increasing the number of neutral 
scattering sites in the mobility model. In this model the number of neutrals is determined 
from the fractional area of the loops involved in scattering. 

8.2 Conclusions 

Laser annealing offers considerable advantage compared to conventional spike 
annealing. Using NLA with multiple pulses increases the activation and increases the 
mobility. This results in a decrease in the sheet resistance with little if any increase in the 



133 

junction depth. Thus, nonmelt laser annealing alone can be used to produce shallow 

junctions with lower resistivity than conventional annealing techniques. 

8.3 Suggestions for Future Work 
Now that the various results of the NLA has been investigated over a variety of 

conditions, more specific studies can be performed to elaborate on some of the details. 
For example, a study involving a wider range of implant energies and doses would give 
more information into the types of defects evolving in the samples. A large implant and 
dose matrix along with post-processing would provide more detailed information on the 
activation energies and concentration of the defects evolving from the NLA. Although, 
studies must be aggressively geared towards the analysis of shallower, heavily doped 
samples. The samples can be at energies less than 1 KeV where the focus would be on 
the electrical activation and BIC formation. Perhaps co-implantation of the boron with 
germanium of fluorine could be used to produce even shallower junctions with more 
abrupt profiles. It would certainly be interesting to investigate the effects of the 
germanium and fluorine presence on the mobility and activation. 

Another interesting idea might be to combine the nonmelt laser anneal with the the 
processes that use laser thermal processing for melting amorphous regions. The first 
requirement would be that a laser with a an absorption depth greater than the amorphous 
crystalline depth would be used. Then, an NLA would be applied to the amorphized 
region prior to the melting laser anneal. Of course, the benefits of multiple pulses should 
be studied. The effect of using the NLA would be an attempt to clean up the amorphous 
crystalline interface prior to melting and regrowth. This technique should show 
improvements over the low-temperature furnace anneals which may not allow for as 
much interface repair due to the low temperatures used. A cleaner/smoother interface 



134 

should reduce the amount of defects in the regrown material. Also, if the laser anneal 
heats the damage beyond the amorphous crystalline interface it may also be possible to 
remove or at least significantly reduce the end-of-range (EOR) damage. The EOR range 
damage results in high leakage currents and may also be a source of interstitials during 
post-processing. Having interstitials available during post-processing will increase boron 
diffusion and the possibility of boron-interstitial clustering and dopant deactivation. 



APPENDIX A 
TEMPERATURE SIMULATION DURING NLA USING FLOOPS 

The following FLOOPS files are used together to model the temperature distribution 
in silicon during the nonmelt laser anneal (NLA): nlaparams.tcl, nlaheating.tcl, 
cooldown.tcl, nlaexample.tcl. The files contain all of the variables and constants used for 
the simulations presented in the work along with comments. The files are desribed and 
presented below. FLOOPS defines the various models required for dopant diffusion in 
the TclLib directory. These files must also be modified to account for the nonuniform 
temperature distribution, Temp. Although, Dopant.tcl, Potential .tcl, Defect.tcl, and 
DefClust.tcl are all used and made dependent on Temp, only Dopant.tcl and Potential .tcl 
are provided as examples to show the changes made to the model files. 

The file, nlaparams.tcl, shows how the parameter database in FLOOPS can be altered 
to accomadate a variable temperature, Temp, for the laser anneal. Using Temp as a 
solution variable allows the temperature distribution to be defined by a set of equations 
instead of using a constant temperature across the entire gridded region. This of course 
requires that the temperature, Temp, be solved for at every time step at each node. Then 
all of the other parameters can be found based on the Temp at the desired node. This 
model along with boron and defect models can be used to simulate the boron diffusion 
and defect evolution in silicon during the NLA. 
nlaparams.tcl: 

proc nlaArrhenius {pre act} { 
setk8.617383e-05 
return "($pre • exp(- 1.0 * $act / ($k * Temp)))" 

135 



136 



} 

pdbSetDouble Silicon Int DO.Pf 0.138 
pdbSetDouble Silicon Int DO.Ea 1.37 
pdbSetDouble Silicon Int Cstr.Pf 3.65652209167e27 
pdbSetDouble Silicon Int Cstr.Ea 3.7 
pdbSetDouble Silicon Int neg.Pf 5.68 
pdbSetDouble Silicon Int neg.Ea 0.48 
pdbSetDouble Silicon Int pos.Pf 5.68 
pdbSetDouble Silicon Int pos.Ea 0.42 
pdbSetDouble Silicon Vac DO.Pf 1 . 1 8e-4 
pdbSetDouble Silicon Vac DO.Ea 0.1 
pdbSetDouble Silicon Vac Cstr.Pf 4.05e+26 
pdbSetDouble Silicon Vac Cstr.Ea 3.97 
pdbSetDouble Silicon Vac neg.Pf 5.68 
pdbSetDouble Silicon Vac neg.Ea 0.145 
pdbSetDouble Silicon Vac pos.Pf 5.68 
pdbSetDouble Silicon Vac pos.Ea 0.455 
pdbSetDouble Silicon Vac dneg.Pf 32.47 
pdbSetDouble Silicon Vac dneg.Ea 0.62 
pdbSetDouble Silicon Boron Solubility. Pf 7.68e22 
pdbSetDouble Silicon Boron Solubility.Ea 0.7086 
pdbSetDouble Silicon Boron Int Binding.Pf 8.0e-23 
pdbSetDouble Silicon Boron Int Binding. Ea -1.0 
pdbSetDouble Silicon Boron Int DO.Pf 0.743 
pdbSetDouble Silicon Boron Int DO.Ea 3.56 
pdbSetDouble Silicon Boron Int Dp.Pf 0.617 
pdbSetDouble Silicon Boron Int Dp.Ea 3.56 
pdbSetDouble Silicon Boron Vac Binding.Pf 8.0e-23 
pdbSetDouble Silicon Boron Vac Binding.Ea -0.5 
pdbSetDouble Silicon Boron Vac DO.Pf 0. 1 86 
pdbSetDouble Silicon Boron Vac DO.Ea 3.56 
pdbSetDouble Silicon Boron Vac Dp.Pf 0. 1 54 
pdbSetDouble Silicon Boron Vac Dp.Ea 3.56 

#Altemate z String 

#Oxide/Boron 

pdbSetString Oxide Boron DOz "([nlaArrhenius 3. 16e-4 3.53]" 

pdbSetString Oxide Boron Dstarz "([nlaArrhenius 3.16e-4 3.53]" 

#Oxide/Boron/Grid 

pdbSetString Oxide Boron Grid ScaleVelz "([nlaArrhenius 1.0 2.14])" 

#Oxide_SiIicon 

pdbSetString Oxide_Silicon Boron Segregationz "([nlaArrhenius 1 126.0 0.91])" 

pdbSetString OxideSilicon Boron Transferz "([nlaArrhenius 1.66e-7 0.0])" 

pdbSetString Oxide_Silicon Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])" 

pdbSetString Oxide_Silicon Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])" 

pdbSetString Oxide_Silicon Vacancy Scalez "([nlaArrhenius 1.87 2.14])" 

#Gas_Oxide 

pdbSetString Gas_Oxide Boron Segregationz "([nlaArrhenius 1 126.0 0.91])" 

pdbSetString Gas_Oxide Boron Transferz "([nlaArrhenius 1.66e-7 0.0])" 

pdbSetString Gas_Oxide Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])" 

pdbSetString Gas_Oxide Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])" 

pdbSetString Gas_Oxide Interstitial KinkSitez "([nlaArrhenius 0. 186 -3.19])" 

pdbSetString Gas_Oxide Interstitial Ksurf2z "([pdbGetString Silicon I DOz] * [pdbGetString Silicon_Ox I 

KinkSitez] * [pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])" 

pdbSetString Gas_Oxide Vacancy Scalez "([nlaArrhenius 1.87 2.14])" 



137 



pdbSetString Gas_Oxide Vacancy KinkSitez "([nlaArrhenius 0. 1 86 -3.19])" 

pdbSetStringGas_Oxide Vacancy Ksurf2z "([pdbGetString Silicon I DOz] * [pdbGetString Silicon_Ox I 

KinkSitez] "[pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])" 

#Interface 

pdbSetString Interface Boron Segregationz "([nlaArrhenius 1 126.0 0.91])" 

pdbSetString Interface Boron Transferz "([nlaArrhenius 1.66e-7 0.0])" 

pdbSetString Interface Interstitial Scalez "([nlaArrhenius 4.7e-2 2.0])" 

pdbSetString Interface Interstitial Injz "([nlaArrhenius 5.56e-3 -0.784])" 

pdbSetString Interface Interstitial KinkSitez "([nlaArrhenius 0.186 -3.19])" 

pdbSetString Interface Interstitial Ksurf2z "([pdbGetString Silicon I DOz] * [pdbGetString Silicon_Ox I 

KinkSitez] * [pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -1.5])" 

pdbSetString Interface Vacancy Scalez "([nlaArrhenius 1.87 2. 14])" 

pdbSetString Interface Vacancy KinkSitez "([nlaArrhenius 0.186 -3.19])" 

pdbSetString Interface Vacancy Ksurf2z "([pdbGetString Silicon I DOz] * [pdbGetString Si_Ox I 

KinkSitez] * [pdbGetString Silicon I Capturez] * [nlaArrhenius 8.0e-23 -0.5])" 

#Silicon/311 

pdbSetString Silicon 3 1 1 Cfz "([nlaArrhenius 6.4e-8 1 .4] * [pdbGetString Silicon I Capturez] 

♦[pdbGetString Silicon I DOz] * [nlaArrhenius 8.0e-23 -1.5] * [nlaArrhenius 8.0e-23 -1.5])" 

pdbSetString Silicon 31 1 Crz "([nlaArrhenius 3.0el5 3.7])" 

pdbSetString Silicon 31 1 Kfz "([nlaArrhenius 2.3e-7 -0.42] * [pdbGetString Silicon I DOz])" 

pdbSetString Silicon 311 Krz "([pdbGetString Silicon 311 Kfz] * [nlaArrhenius 4.5e24 2.52])" 

#Silicon/Dall 

pdbSetString Silicon Dall KRpz "([nlaArrhenius 1.84351726123e-08 1.69727351512])" 

#Silicon/Interstitial 

pdbSetString Silicon Interstitial DOz "([nlaArrhenius 0.138 1 .37])" 

pdbSetString Silicon Interstitial Cstarz "([nlaArrhenius [expr 5.0e22*exp(l 1.2)] 3.7])" 

pdbSetString Silicon Interstitial negativez "([nlaArrhenius 5.68 0.48])" 

pdbSetString Silicon Interstitial positivez "([nlaArrhenius 5.68 0.42])" 

#Silicon/Vacancy 

pdbSetString Silicon Vacancy DOz "([nlaArrhenius 1 . 1 8e-4 0. 1 ])" 

pdbSetString Silicon Vacancy Cstarz "([nlaArrhenius [expr 5.0e22*exp(9.0)] 3.97])" 

pdbSetString Silicon Vacancy negativez "([nlaArrhenius 5.68 0.145])" 

pdbSetString Silicon Vacancy positivez "([nlaArrhenius 5.68 0.455])" 

pdbSetString Silicon Vacancy dnegativez "([nlaArrhenius 32.47 0.62])" 

#Gas/Grid/Info 

pdbSetString Gas Grid ScaleVelz "([nlaArrhenius 1.0 2.14])" 

#Oxide/Grid/Info 

pdbSetString Oxide Grid ScaleVelz "([nlaArrhenius 1.0 2.14])" 

#Refractory/Grid/Info 

pdbSetString Refractory Grid ScaleVelz "([nlaArrhenius 1.0 2.14])" 

#Silicon/Boron 

pdbSetString Silicon Boron Interstitial DOz "([nlaArrhenius 0.743 3.56])" 

pdbSetString Silicon Boron Interstitial Dpz "([nlaArrhenius 0.617 3.56])" 

pdbSetString Silicon Boron Vacancy Bindingz "([nlaArrhenius 8.0e-23 -0.5])" 

pdbSetString Silicon Boron Vacancy DOz "([nlaArrhenius 0.186 3.56])" 

pdbSetString Silicon Boron Vacancy Dpz "([nlaArrhenius 0.154 3.56])" 

pdbSetString Silicon Boron Dpz "([pdbGetString Silicon B I Dpz] + [pdbGetString Silicon B V Dpz])" 

pdbSetString Silicon Boron DOz "([pdbGetString Silicon B I DOz] + [pdbGetString Silicon B V DOz])" 

pdbSetString Silicon Boron Dstarz "([pdbGetString Silicon B I DOz] + [pdbGetString Silicon B I Dpz] + 

[pdbGetString Silicon B V DOz] + [pdbGetString Silicon B V Dpz] )" 

pdbSetString Silicon Boron Fiz "( ([pdbGetString Silicon B I DOz] + [pdbGetString Silicon B I Dpz]) / 

[pdbGetString Silicon B Dstarz] )" 

pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 0.7086])" 

pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 0.7086])" 

pdbSetString Silicon Boron Solubilityz "([nlaArrhenius 7.68e22 0.7086])" 

pdbSetString Silicon Boron Interstitial Bindingz "([nlaArrhenius 8.0e-23 -1.0])" 



138 



#Silicon/Grid/Info 

pdbSetString Silicon Grid ScaleVelz "([nlaArrhenius 1.0 2.14])" 

proc nlaDiffLimit {Mat Species Barrier} { 
set Dbase 0.0 
foreach sol $Species { 

set Dbase "(SDbase + ([pdbGetString $Mat $sol DOz]))" 

} 

set Lspa [pdbGetDouble $Mat LatticeSpacing] 

return "[nlaArrhenius "(4.0 * 3.14159 * $Dbase * $Lspa)" SBarrier]" 

> 

proc nlaConcBind {Mat Entropy Binding} { 
set Dens [pdbGetDouble $Mat LatticeDensity] 
return "[nlaArrhenius [expr SDens * exp(SEntropy)] SBinding]" 

} 

proc nlaSurfDiffLimit {Mat Side Sol Barrier} { 
set Dbase "([pdbGetString SSide $Sol DOz])" 
set Lspa [pdbGetDouble SSide LatticeSpacing] 
set Kink [pdbGetDouble SMat $Sol KinkSite] 

return "[nlaArrhenius "(3.14159 * SDbase * $Lspa * $Kink)" SBarrier]" 

} 

#set the parameters 

pdbSetString Si Potential Permittivityz "11.7" 

#from Martin Green's JAP paper 

proc nlaGreenBandGap {} {return "(1.2060 - 2.73e-4 * Temp - 1.4e-8 * Temp * Temp)"} 

proc nlaSiliconNc {} { 

seth6.62617e-34 

set mO 0.91 095e-30 

set temp [simGetDouble Diffuse tempK] 

set mdt "0.1905 * $m0 * 1 .2060 / ([nlaGreenBandGap])" 

set mdl [expr 0.9163 * $m0] 

set md "exp( log( 36.0 * ($mdt) * (Smdt) * $mdl ) / 3.0 )« 

setval "2 * 3.141592654 * ($md) * 1.38066e-23 * Temp/($h * $h)" 

return "(($val) * sqrt($val) * 2.0e-6)" 
} 

pdbSetString Si Potential Ncz "[nlaSiliconNc]" 

proc nlaSiliconNv {} { 

seth6.62617e-34 

set mO 0.91 095e-30 

set temp [simGetDouble Diffuse tempK] 

settl "(0.4435870+Temp* (0.3609528e-2+ 
Temp*(0. 1 1 735 1 5e3+Temp*(0. 1 26321 8e5+Temp*0.302558 le-8))))" 

set t2 "(1 ,0+Temp*(0.4683382e-2+Temp*(0.2286895e-+Temp*(0.7469271 e6+Temp*0. 1 72748 1 e8))))" 

set md "exp( log($tl/$t2) ♦ 2.0/3.0) * $m0 " 

set val "(2 * 3.141592654 * ($md) * 1.38066e-23 * Temp / ($h * $h))" 

return "($val * sqrt($val) * 2.0e-6)" } 



139 



pdbSetString Si Potential Nvz "[nlaSiliconNv]" 

pdbSetString Vtiz "(1.0/(8.617383e-05*Temp))" 

pdbSetString Si Potential niz "sqrt(([pdbGetString Si Potential Ncz])*([pdbGetString Si Potential Nvz])) * 
exp( -0.5 * ([nlaGreenBandGap]) * ([pdbGetString Vtiz]))" 

setk 8.617383e-05 

pdbSetString Oxide_Silicon Interstitial thetaz "0.0" 

pdbSetString Oxide_Silicon Interstitial Kratz "0.0" 

pdbSetString Oxide_Silicon 12 Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Silicon 12 0.0]])" 

pdbSetString OxideSilicon Interstitial Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Si Int 0.0])" 

pdbSetString Oxide_Silicon Interstitial Ktrapz "(10.0*[nlaSurfDiffLimit Oxide_Silicon Si Int 0.0])" 

pdbSetString Oxide_Silicon V2 Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Silicon V2 0.0])" 

pdbSetString Oxide_Silicon Vacancy Ksurfz "([nlaSurfDiffLimit Oxide_Silicon Si Vac 0.0])" 

pdbSetString OxideSilicon Vacancy Ktrapz "(10.0*[nlaSurfDiffLimit Oxide_Silicon Si Vac 0.0])" 

pdbSetString Silicon C31 1 Bindlz "([nlaConcBind Silicon 4.8 2.275])" 
pdbSetString Silicon 12 Bindz "([nlaConcBind Si 0.0 2.0])" 
pdbSetString Silicon 14 Bindz "[nlaConcBind Si 0.0 0.8]" 
pdbSetString Silicon 16 Bindz "[nlaConcBind Si 0.0 0.8]" 
pdbSetString Silicon Smic Bindz "[nlaConcBind Silicon 1 1.9 2.1]" 
pdbSetString Silicon V2 Bindz "[nlaConcBind Si 0.0 2.5]" 

pdbSetString Silicon C31 1 KnI2z "[nlaDiffLimit Silicon 12 1.1]" 
pdbSetString Silicon C31 1 KfI2z "[nlaDiffLimit Silicon 12 0.0]" 
pdbSetString Silicon C31 1 Kflz "[nlaDiffLimit Silicon Int 0.1]" 
pdbSetString Silicon C31 1 KfV2z "[nlaDiffLimit Silicon V2 0.0]" 
pdbSetString Silicon C31 1 KfVz "[nlaDiffLimit Silicon Vac 0.0]" 
pdbSetString Silicon 12 Kforwardz "[nlaDiffLimit Si Int 0.0]" 
pdbSetString Silicon 12 KRecombz "[nlaDiffLimit Si {12 Vac} 0.0]" 
pdbSetString Silicon 12 KBiMolez "(0.5*[nlaDiffLimit Si {V2 12} 0.0])" 
pdbSetString Silicon 14 Kforwardz "(4.0 * [nlaDiffLimit Si 12 0.0])" 
pdbSetString Silicon 14 KRecombz "(4.0*[nlaDiffLimit Si V2 0.0])" 
pdbSetString Silicon 16 Kforwardz "(6.0 * [nlaDiffLimit Si 12 0.0])" 
pdbSetString Silicon 16 KRecombz "(6.0*[nlaDiffLimit Si V2 0.0])" 
pdbSetString Silicon Smic Kflz "[nlaDiffLimit Silicon Int 0.0]" 
pdbSetString Silicon V2 Kforwardz "[nlaDiffLimit Si Vac 0.3]" 
pdbSetString Silicon V2 KRecombz "[nlaDiffLimit Si {V2 Int} 0.0]" 
pdbSetString Silicon V2 KBiMolez "(0.5*[nlaDiffLimit Si {V2 12} 0.0])" 

pdbSetString Silicon Boron Interstitial Kratez "[nlaDiffLimit Silicon Int 0.0]" 
pdbSetString Silicon Boron Vacancy Kratez "[nlaDiffLimit Silicon Vac 0.0]" 
#pdbSetString Silicon Phosphorus Interstitial Krate "[nlaDiffLimit Si Int 0.0]" 

proc nlalnitDefect {} { 
# SetTemp 

#turn on the defects 

pdbSetSwitch Si I DiffModel Numeric 

pdbSetSwitch Si V DiffModel Numeric 

solution name = Int solve (damp ! negative 

solution name = Vac solve (damp [negative 

sel z= [pdbGetString Si I Cstarz] name=Int store 
sel z= [pdbGetString Si V Cstarz] name=Vac store } 



140 



#create cluster solution variables 

solution add name=I2 ifpresent = "Int 12" !damp (negative 

pdbSetString Si 12 EquationProc 2Defect 

pdbSetString Si 12 InitProc Defectlnit 

pdbSetString Ox_Si 12 EquationProc 2Bound 

solution add name=C3 1 1 ifpresent = "Int 12 C3 11 " ! damp Inegative 
solution add name=D3 1 1 ifpresent = "Int 12 D3 11 " ! damp ! negative 
solution add name=Smic ifpresent = "Int 12 Smic" Idamp Inegative 
pdbSetString Si C31 1 EquationProc 31 lEqn 
pdbSetString Si C3 1 1 InitProc C3 1 Unit 

solution add name=V2 ifpresent = "V2 Vac" Inegative 
pdbSetString Si V2 EquationProc 2Defect 
pdbSetString Si V2 InitProc Defectlnit 
pdbSetString Ox_Si V2 EquationProc 2Bound 

proc nlalnitCluster {} { 
solution addname=I2 solve Idamp Inegative 
solution addname=V2 solve Idamp Inegative 
sel z = [pdbGetString Si 12 Cstarz] name = 12 store 
sel z = [pdbGetString Si 14 Cstarz] name = 14 store 
sel z = [pdbGetString Si V2 Cstarz] name = V2 store 
sel z = 1 .0 name = D3 1 1 store 

} 



The file, nlaheating.tcl sets up the parameters to determine how the temperature, 
Temp, will vary during the laser anneal, 
nlaheating.tcl: 

#the parameters are all functions of 
#temperature. the analytical fits to data 
#are given, if used you will have trouble 
#converging when boron and defects added, so, 
#use the average values which are close to 
#room temp values. 

#density kg/cm3 
set p 2.33 

#thermal conductivity W/cm-K 
#Km meters. . . Kcm cm. . . K(Temp) 
#set Km "2.99e4/(Temp-99.0)" 
#setKcm"$Km*1.0e-2" 
set K 0.6 

#thermal capacity J/kg-K 

#Cp also a function of Temp... 

#set Cp "(1.4743+5.689e-4*Temp)*1.0e6/$p" 

set Cp 0.7 

#latentheat... if phase change... J/kg 



141 



#set deltah 1.4e6 

#absorption coefficient, 1/cm 

set al 4.4e4 

set a2 [expr $al/1.0e4] 

#1 /absorption depth is temp dependent 

#this will work for temp only but never 

#converges with boron and defects... 

#setal 0.8e4 

#set al "$al*exp((Temp-300.0)/430.0)" 

#seta2"$al/1.0e4" 

#you can use the variable R too, but 
#no significant change... if you use 
#R(Temp) then you need to adjust al 
#setR"0.5+5.0e-5*Temp" 
set R 0.5 

#laser intensity W/cm2 
set J 0.35 

set plength 20.0e-9 
set I [expr $J/$plength] 

pdbSetString Si Temp Equation "(-$K*grad(Temp)-$I*(1.0-$R)*$al *exp(-$a2*x)+ddt($p*$Cp*Temp))" 
sel z=300 name=Temp store 

The file, cooldown.tcl, sets up the parameters to determine how the temperature, 

Temp, will vary during the cooldown after the laser is turned off. 

cooldown.tcl: 

#sigma is the stefan-boltzmann constant (W*cm-2*K-4) convert 

#to microns... 

#set sigma [expr (5.67e-12)*1.0e-8] 

setsigma5.67e-12 

#need to know volume of piece/wafer being cooled 
#set volume [expr 1.0*1. 0el2] 
set volume 0.001 

#need to know area in contact with air 
#set area [expr 1.0/1. Oe-8] 
set area 1.0 

#emissivity of silicon (black body=max of 1) 
set e 0.1 

#setK0.76 
set pC 2.33 
set cpC 0.9 

pdbSetString Oxide_Silicon Temp EquationSilicon "$e * Ssigma * $area / (Svolume * $pC *$cpC) * 
Temp_Silicon A 4.0" 



142 
pdbSetString Silicon Temp Equation "- $pC * ScpC * ddt(Temp) + $K * grad(Temp) 

The file simplecooldown.tcl is included which shows an equation for Temp used to aid 
in convergence. The equation is a simpler analytical fit found to the define the cooldown. 
This file will speed up the simulation, 
simplecooldown.tcl: 

#sigma is the stefan-boltzmann constant (W*cm-2*K-4) 
setsigma5.67e-12 

#need to know volume of piece/wafer being cooled 
set volume 0.001 

#need to know area in contact with air 
set area 2.0 

#emissivity of silicon (black body=max of 1) 
#silicon is a gray body include(Temp) if you want. 
set e 0.4 

#set in heatingparams.tcl 
set p 2.33 
set Cp 0.7 
set K 0.6 

pdbSetString Silicon Temp Equation "$p * $Cp * ddt(Temp) - $K * grad(Temp)" 
pdbSetString Oxide_Silicon Temp Equation_Silicon "-1.0e-2*Temp A 2" 

The file, nlaexample.tcl, reads in nlaparams.tcl to set up the required parameters for 
boron and defect diffusion. A grid is generated and boron implanted. Temp is added to 
the list of solution variables. The initial interstitial profile is assumed to be equal to the 
boron as-implanted profile. The file is set up for 1000 pulses at 20 ns/pulse with a 
frequency of 100 Hz. During the NLA the Temp equation is set by sourcing the file 
nlaheating.tcl and an initial temperature of 300K. After the NLA the silicon is defined to 
cool according to the parameters defined in cooldown.tcl (or simplecooldown.tcl). 
nlaexample.tcl: 

math diffuse dim=l umf none triplet 
source ~ske/source/nlaparams.tcl 
source ~ske/myfloops/TclLib/Dopant.tcl 



143 



source ~ske/myfloops/TclLib/Potential.tcl 
source ~ske/my floops/TclLib/Def ect. tcl 
source ~ske/myfloops/TclLib/DefClust.tcl 

pdbSetString Si Boron InitProc InitDopant 
solution name=Potential damp 

pdbSetSwitch Si I DifiModel Numeric 
pdbSetSwitch Si V DifiModel Numeric 
solution name = Int solve !damp Inegative 
solution name = Vac solve !damp Inegative 

pdbSetDouble Silicon Int Dp [pdbDelayDouble Si Int DO] 
pdbSetDouble Ox_Si Int Ksurf {[Arrhenius 1.95 2.5]} 

line x loc=-0.01 tag=oxi spac=0.01 

line x loc=0.0 tag=top spac=0.001 

line x loc=0.4 spac=0.001 

line x loc=1.0 tag=bot spac=0.05 

#line x loc=50.0 spac=1.0 

#line x loc=100.0 tag=bot spac=5.0 

region silicon xlo=top xhi=bot 

region oxide xlo=oxi xhi=top 

init 

implant dose=2.0el5 energy=5 boron ang=7 

set roomtemp 25 

sel z=($roomtemp+273.0) name=Temp store 

SetTemp Sroomtemp 

InitDefect Sroomtemp 

pdbSetSwitch Si Boron DifiModel React 

sel z=Boron name=Int store 

set CompGraph [CreateGraph Window] 

selz=loglO(Boron) 

CreateLine SCompGraph Aslmplanted [slice silicon] 

set pulsemin [expr 20e-9/60.0] 
set freq[expr 100.0*60.0] 

plot.xy min = {0 0} max= {1000 lel6} 

global ct 

set ct [open 5KeV2el5PairDosedata w] 

for {seti 1} {$i <= 1000} {incri} { 

sel z=300.0 name=Temp store 

source nlaheating.tcl 

diffuse temp=$roomtemp time=$pulsemin init=le-12 

source cooldown.tcl 

diffuse temp=$roomtemp time=[expr 1.9e-4/60.0-$pulsemin] init=le-12 

pdbSetString Silicon Temp Equation "Temp" 
sel z=300 name=Temp store 



144 

diffuse temp=$roomtemp time=[expr 1.0/$freq-1.9e-4/60.0-$puIsemin] init=le-12 

sel z=Int 

set IntDose [FindDose] 

sel z=Boron+BoronInt+BoronVac 

set TotalBoronDose [FindDose] 

sel z=BoronActive 

set BoronActiveDose [FindDose] 

point.xy x = $i y = SIntDose name = IntDose 

point.xy x = $i y = STotalBoronDose name = TotalBoronDose 

point.xy x = $i y = SBoronActiveDose name = BoronActiveDose 

puts -nonewline $ct $i 

puts -nonewline $ct " " 

puts -nonewline $ct SIntDose 

puts -nonewline Set " " 

puts -nonewline Set STotalBoronDose 

puts -nonewline Set " " 

puts -nonewline Set SBoronActiveDose 

puts -nonewline Set " " 

puts Set " " 

flush Set 

} 

selz=loglO(Boron) 

CreateLine SCompGraph Pair 1000 [slice silicon] 

Dopant.tcl: 

proc InitDopant {Mat Sol} { 
set pdbMat [pdbName SMat] 

set model [pdbGetSwitch SpdbMat SSol DiffModel] 

#if we have the react model, we need to set up solutions 
if{$model==3} { 

#get a list of defects we react with 

set Id [pdbGetString SpdbMat SSol Defects] 

foreach d Sid { 
solution add name = ${Sol}${d} solve !damp (negative 

} 

puts "Reaction Model for SSol" 

#else we need to make sure things are clear! 
} else { 

#get a list of defects we react with 

set Id [pdbGetString SpdbMat SSol Defects] 

foreach d Sid { 

solution name = ${Sol}${d} nosolve !damp (negative 
} 
} 
} 

proc DopantBulk { Mat Sol } { 



145 



set k 8.617383e-05 

set pdbMat [pdbName $Mat] 
puts"DopantBulkl" 
#work with the active model - create DopantActive... 
set ActModel [pdbGetS witch SpdbMat $Sol ActiveModel] 
set ActName $ {Sol {Active 
if{SActModel = 0} { 

term name = SActName add eqn = $Sol $Mat 
}elseif{$ActModel = l} { 

set ssPf [pdbGetDouble SpdbMat $Sol Solubility.Pf] 

set ssEa [pdbGetDouble SpdbMat SSol SoIubility.Ea] 

set ss "(SssPf * exp(- 1.0* SssEa / ($k * Temp)))" 

term name = SActName add eqn = "$ss * SSol / (Sss + SSol)" SMat 

} else { 

#need to add dynamic precipitation here! 

set ssPf [pdbGetDouble SpdbMat SSol Solubility.Pf] 

set ssEa [pdbGetDouble SpdbMat SSol SoIubility.Ea] 

set ss "(SssPf * exp(- 1.0 * SssEa / ($k * Temp)))" 

term name = SActName add eqn = "Sss * SSol / (Sss + SSol)" SMat 

} 

puts "DopantBulk2" 
set model [pdbGetSwitch SpdbMat SSol DiffModel] 
set ChgName 
if {$model==0} { 

set ChgName [DopantConstant SMat SSol] 
} elseif {$model=l} { 

set ChgName [DopantFermi SMat SSol] 
} elseif {Smodel = 2} { 

set ChgName [DopantPair SMat SSol] 
} elseif {Smodel = 3} { 
puts "calling DopantReact" 

set ChgName [DopantReact SMat SSol] 
} 

puts "DopantBulk3" 
#set up charged species in potential equation 
set chgtype [pdbGetSwitch SpdbMat SSol Charge] 
set chg [term name=Charge print SMat] 
if {[lsearch Schg SChgName] == -1 } { 
#acceptor 
if {$chgtype=l} { 

term name = Charge add eqn = "Schg - SChgName" SMat 
#donor 

} elseif {Schgtype = 2} { 
term name = Charge add eqn = "Schg + SChgName" SMat 

} 
#neutrals 

} elseif {Schgtype — 0} {} 
} 



146 



proc DopantConstant { Mat Sol } { 
setk 8.617383e-05 

set pdbMat [pdbName $Mat] 
set DOIPf [pdbGetDouble SpdbMat $Sol I DO.Pf] 
set DOffia [pdbGetDouble SpdbMat $Sol I DO.Ea] 
set diffDI "(SDOIPf * exp(- 1.0 * SDOIEa / ($k * Temp)))" 
set DOVPf [pdbGetDouble SpdbMat $Sol V DO.Pf] 
set DOVEa [pdbGetDouble SpdbMat SSol V DO.Ea] 
set diffOV "(SDOVPf * exp(- 1.0 * SDOVEa / ($k * Temp)))" 
set DpIPf [pdbGetDouble SpdbMat SSol I Dp.Pf] 
set Dpffia [pdbGetDouble SpdbMat SSol I Dp.Ea] 
set diffpl "(SDpIPf * exp(- 1.0 * SDpIEa / ($k * Temp)))" 
set DpVPf [pdbGetDouble SpdbMat SSol V Dp.Pf] 
set DpVEa [pdbGetDouble SpdbMat SSol V Dp.Ea] 
set diffpV "(SDpVPf * exp(- 1.0 * SDpVEa / ($k * Temp)))" 
set diff "(SdiffOI + SdiffOV + Sdiffpl + SdiffpV)" 
set ActName ${ Sol} Active 

puts "DopantConstant" 

pdbSetString SpdbMat SSol Equation "ddt(SSol) - Sdiff * grad( SActName )" 
return SActName 
} 

proc DopantFermi { Mat Sol } { 

set pdbMat [pdbName SMat] 
setk 8.617383e-05 

#build the diffusivity 

set difnam DiffSSol 

puts "DopantFermi 1" 
#build the diffusivity term 

# set dif [pdbGetDouble SMat SSol DO] 

set DOIPf [pdbGetDouble SpdbMat SSol I DO.Pf] 

set DOffia [pdbGetDouble SpdbMat SSol I DO.Ea] 

set diffDI "(SDOIPf * exp(- 1.0 * SDOIEa/ ($k * Temp)))" 

set DOVPf [pdbGetDouble SpdbMat SSol V DO.Pf] 

set DOVEa [pdbGetDouble SpdbMat SSol V DO.Ea] 

set diffOV "(SDOVPf * exp(- 1.0* SDOVEa / ($k * Temp)))" 

set dif "(SdiffOI + SdiffOV)" 

puts "DopantFermi2" 
if {[pdblsAvailable SMat SSol Dn]} { 

set dif "Sdif + [pdbGetDouble SMat SSol Dn] * Noni" 

} 

if {[pdblsAvailable SMat SSol Dnn]} { 

set dif "Sdif + [pdbGetDouble SMat SSol Dnn] * Noni A 2" 
} 
if {[pdblsAvailable SMat SSol Dp]} { 

# set dif "Sdif + [pdbGetDouble SMat SSol Dp] * Poni" 
set DpIPf [pdbGetDouble SpdbMat SSol I Dp.Pf] 

set Dpffia [pdbGetDouble SpdbMat SSol I Dp.Ea] 
set diffpl "(SDpIPf * exp(- 1.0 * SDpIEa / ($k * Temp)))" 
set DpVPf [pdbGetDouble SpdbMat SSol V Dp.Pf] 
set DpVEa [pdbGetDouble SpdbMat SSol V Dp.Ea] 



147 



set diffpV "($DpVPf * exp(- 1.0 * SDpVEa / ($k * Temp)))" 
set dif2 "(Sdiffpl + SdiffpV] 

# set dif "$dif + [pdbGetDouble SMat SSol Dp] * Poni" 
set dif"$dif+$dif2* Poni" 

} 

if {[pdblsAvailable SMat SSol Dpp]} { 

set dif "$dif + [pdbGetDouble SMat $Sol Dpp] * Poni A 2" 

} 

puts "Ferimnear3" 

# set difnam "$dir 

term name = Sdifnam add eqn = "$dif SMat 

puts "DopanfFermi3" 
set ActName ${ Sol} Active 
set eqn "ddt(SSol) - Sdifnam * grad( SActName )" 
set chgtype [pdbGetSwitch SpdbMat SSol Charge] 
if {$chgtype = l} { 

# set difnam "Sdif/ Poni" 

term name = Sdimam add eqn = "(Sdif) / Poni" SMat 
set eqn "ddt(SSol) - Sdifnam * grad( SActName * Poni )" 
} elseif {$chgtype = 2} { 

# set difnam "Sdif/ Noni" 

term name = Sdifnam add eqn ■ "(Sdif) / Noni" SMat 
set eqn "ddt(SSol) - Sdifnam * grad( SActName * Noni )" 
} 

pdbSetString SpdbMat SSol Equation Seqn 
return SActName 
} 



proc DopantDefectPair { Mat Sol Def } { 
setk 8.617383e-05 
set pdbMat [pdbName SMat] 
puts "DopantDefectPair SMat SSol SDef" 

#buld the diffusivity 

set difnam Diff${Sol}${Def} 

#build the diffusivity term 

# set dif [pdbGetDouble SMat SSol SDef DO] 

set DOPf [pdbGetDouble SpdbMat SSol SDef DO.Pf] 
set DOEa [pdbGetDouble SpdbMat SSol SDef DO.Ea] 
set dif "(SDOPf * exp(- 1.0* SDOEa / ($k * Temp)))" 

if {[pdblsAvailable SMat SSol SDef Dn]} { 

# set dif "Sdif + [pdbGetDouble SMat SSol SDef Dn] * Noni" 

set DnPf [pdbGetDouble SpdbMat SSol SDef Dn.Pf] 

set DnEa [pdbGetDouble SpdbMat SSol SDef Dn.Ea] 

set dif "(Sdif + (SDnPf * exp(- 1.0 * SdnEa / ($k * Temp))) * Noni)" 

} 

if {[pdblsAvailable SMat SSol Dnn]} { 

# set dif "Sdif + [pdbGetDouble SMat SSol SDef Dnn] * Noni A 2" 

set DnnPf [pdbGetDouble SpdbMat SSol SDef Dnn.Pf] 
set DnnEa [pdbGetDouble SpdbMat SSol SDef Dnn. Ea] 









148 

set dif "($dif + (SDnnPf * exp(- 1.0* SDnnEa / ($k * Temp))) * Noni A 2)" 

} 

if {[pdbls Available $Mat$Sol Dp]} { 

# set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dp] * Poni" 

set DpPf [pdbGetDouble SpdbMat $Sol SDef Dp.Pf] 

set DpEa [pdbGetDouble SpdbMat $Sol SDef Dp.Ea] 

set dif "(Sdif + ($DpPf * exp(- 1.0 * SDpEa / ($k * Temp))) * Poni)" 

} 

if {[pdbls Available $Mat $Sol Dpp]} { 

# set dif "$dif + [pdbGetDouble $Mat $Sol $Def Dpp] * Poni A 2" 

set DppPf [pdbGetDouble SpdbMat $Sol SDef Dpp.Pf] 

set DppEa [pdbGetDouble SpdbMat SSol SDef Dpp.Ea] 

set dif "(Sdif + (SDppPf * exp(- 1 .0 * SDppEa / ($k * Temp))) * Poni A 2)" 

} 

setSubName${Sol}Sub 

set chgtype [pdbGetSwitch SMat SSol Charge] 

setchg 1.0 

if {$chgtype==l} { 

set chg Poni 
Jelseif {$chgtype==2} { 

set chg Noni 

} 

puts Sdif 

term name = Sdifnam add eqn = "( Sdif ) / Schg" SMat 

set eqn "Sdifnam * grad( SSubName * Scale${Def} * Schg )" 
term name = Flux${Sol}${Def} add eqn = Seqn SMat 
puts "SSol Seqn" 

set de [pdbGetString SMat SSol Equation] 

pdbSetString SMat SSol Equation "Sde - Flux${Sol}${Def}" 

set de [pdbGetString SMat SDef Equation] 

# set bind [pdbGetDouble SMat SSol SDef Binding] 

set BinPf [pdbGetDouble SpdbMat SSol SDef Binding.Pf] 
set BinEa [pdbGetDouble SpdbMat SSol SDef BindingEa] 
set bind "(SBinPf * exp(- 1 .0 * SBinEa / ($k * Temp)))" 
pdbSetString SMat SDef Equation "Sde + ddt($bind * SSubName * SDef) - Flux${Sol}${Def}" 

} 

proc DopantPair { Mat Sol } { 
setk 8.617383e-05 
set pdbMat [pdbName SMat] 

#get all of the defects we are working with 
set Id [pdbGetString SpdbMat SSol Defects] 

*ft>uild an expression for the substitutional dopant 
set ActName ${ Sol} Active 
set den 1.0 
foreach d Sid { 

# set den "Sden + $d * [pdbGetDouble SpdbMat SSol $d Binding]" 
set BindingPf [pdbGetDouble SpdbMat SSol $d Binding.Pf] 

set BindingEa [pdbGetDouble SpdbMat SSol $d BindingEa] 

set Bindingd "(SBindingPf * exp(- 1 .0 * SBindingEa / ($k * Temp)))" 

set den "Sden + $d * SBindingd" 

} 



149 



term name = ${Sol}Sub add eqn = "SActName / ( $den )" $Mat 

#create the basic equation and then add 
pdbSetString SpdbMat $Sol Equation "ddt( $Sol )" 

#for each dopant defect pair, build the flux 
foreach d $ld { 

DopantDefectPair SpdbMat $Sol $d 

} 

puts [pdbGetString SpdbMat $Sol Equation] 

return ${ Sol} Sub 

} 



proc Segregation { Mat Sol } { 
setk 8.617383e-05 
set pdbMat [pdbName $Mat] 

#get the names of the sides 
set si [FirstMat SpdbMat] 
set s2 [SecondMat SpdbMat] 

set ssl [pdblsAvailable $sl $Sol DiffModel] 
set ss2 [pdblsAvailable $s2 $Sol DiffModel] 

if { $ssl && $ss2 } { 

puts "SpdbMat $Sol" 

set seg [pdbGetString SpdbMat $Sol Segregationz] 
set trn [pdbGetString SpdbMat SSol Transferz] 
puts "Sseg Stm" 

setsml ${Sol}_$sl 
setsm2${Sol}_$s2 
set eq M $tm * (Ssml - $sm2 / $seg)" 
pdbSetString SpdbMat SSol Equation_$sl "- Seq" 
pdbSetString SpdbMat SSol Equation_$s2 "Seq" 
} 
} 

proc DopantDefectReact { Mat Sol Def } { 
setk 8.617383e-05 

puts "DopantDefectReact SMat SSol SDef ' 

setS${Sol}${Def} 

set pdbMat SMat 

#assume the dopant-defect diffusivity is constant 

set BinPf [pdbGetDouble SpdbMat SSol SDef Binding.Pf] 

set BinEa [pdbGetDouble SpdbMat SSol SDef Binding.Ea] 

set B "(SBinPf * exp(- 1.0 * SBinEa / ($k * Temp)))" 

set CsPf [pdbGetDouble SpdbMat SDef Cstr.Pf] 



150 

set CsEa [pdbGetDouble SpdbMat SDef Cstr.Ea] 

set Cs "($CsPf * exp(- 1 . * SCsEa / ($k * Temp)))" 

set DOPf [pdbGetDouble SpdbMat SSol $Def DO.Pf] 
set DOEa [pdbGetDouble SpdbMat $Sol $Def DO.Ea] 
set DO "(SDOPf * exp(- 1 .0 * $DOEa / ($k * Temp)))" 

setdax"$DO/($B*$Cs) H 
puts "predax" 
puts $dax 

#build the effective charge state dependent binding 

set Bind 1 

if {[pdbls Available $Mat $Sol $Def Dn]} { 

# set Bind "SBind + [pdbGetDouble $Mat $Sol $Def Dn] * Noni / $D0" 

set DnPf [pdbGetDouble SpdbMat $Sol $Def Dn.Pf] 
set DnEa [pdbGetDouble SpdbMat SSol SDef Dn.Ea] 
set Dn "(SDnPf * exp(- 1.0 * SDnEa / ($k * Temp)))" 
set Bind "SBind + SDn * Noni / SDO" 

} 

if {[pdbls Available SMat SSol Dnn]} { 

# set Bind "SBind + [pdbGetDouble SMat SSol SDef Dnn] * Noni A 2 / $D0" 

set DnnPf [pdbGetDouble SpdbMat SSol SDef Dnn.Pf] 
set DnnEa [pdbGetDouble SpdbMat SSol SDef Dnn.Ea] 
set Dnn "(SDnnPf * exp(- 1.0 * SDnnEa / ($k * Temp)))" 
set Bind "SBind + SDnn * Noni A 2 / SDO" 

} 

if {[pdblsAvailable SMat SSol Dp]} { 

# set Bind "SBind + [pdbGetDouble SMat SSol SDef Dp] * Poni / SDO" 

set DpPf [pdbGetDouble SpdbMat SSol SDef Dp.Pf] 
set DpEa [pdbGetDouble SpdbMat SSol SDef Dp.Ea] 
set Dp "(SDpPf * exp(+ 1.0 * SDpEa / ($k * Temp)))" 
set Bind "SBind + SDp * Poni / SDO" 

} 

if {[pdblsAvailable SMat SSol Dpp]} { 

# set Bind " SBind + [pdbGetDouble SMat SSol SDef Dpp] * Poni A 2 / SDO" 

set DppPf [pdbGetDouble SpdbMat SSol SDef Dpp.Pf] 
set DppEa [pdbGetDouble SpdbMat SSol SDef Dpp.Ea] 
set Dpp "(SDppPf * exp(- 1.0 * SDppEa / ($k * Temp)))" 
set Bind "SBind + $Dpp * Poni A 2 / SDO" 

} 

setSubName${Sol}Sub 

set chgtype [pdbGetSwitch SMat SSol Charge] 

set chg 1.0 

if {$chgtype==l} { 

set chg Poni 
} elseif {Schgtype = 2} { 

set chg Noni 

} 

puts Sdax 

set flux "Sdax * grad( $S * Schg ) / Schg" 

puts Sflux 

puts SBind 

#build the reaction 



151 



set K [pdbGetString $Mat SSol $Def Kratez] 

term name = ReactSS add eqn = "$K * (${Sol}Sub * $Def - ${Sol}${Def} / ($B * (SBind)))" $Mat 

set de [pdbGetString $Mat SSol Equation] 
pdbSetString $Mat $Sol Equation "$de + ReactSS" 
set de [pdbGetString $Mat $Def Equation] 
pdbSetString $Mat $Def Equation "$de + ReactSS" 

pdbSetString SMat ${Sol}${Def} Equation "ddt($S) - Sflux - ReactSS" 
} 



proc DopantReact { Mat Sol } { 
setk 8.617383e-05 
set pdbMat [pdbName SMat] 

#get all of the defects we are working with 
set Id [pdbGetString SpdbMat SSol Defects] 

#see if we have created a substitutional solution variable 

set ActName $ {Sol} Active 
set den SActName 
foreach d Sid { 

setden"Sden-${Sol}${d}" 

} 

term name = ${Sol}Sub add eqn = "Sden" SMat 

puts "Substitutional is [term name = ${ Sol} Sub SMat print]" 

#create the basic equation and then add to it 
pdbSetString SpdbMat SSol Equation "ddt( SSol )" 
puts [pdbGetString SpdbMat SSol Equation] 

#for each dopant defect pair, build the flux 

foreach d Sid { 

puts "calling DopantDefectReact" 
DopantDefectReact SpdbMat SSol $d 
puts "return from DopantDefectReact" 

} 
puts "you made it here" 
puts [pdbGetString SpdbMat SSol Equation] 

return ${Sol}Sub 
} 

Potential.tcl: 

proc PotentialEqns { Mat Sol } { 
set pdbMat [pdbName SMat] 
set Vti "(1.0/(8.61 7383e-05*Temp))" 

set terms [term list] 

if {[lsearch Sterms Charge] = -1 } { 

term name = Charge add eqn = 0.0 SMat 

} 



152 



set Poiss 

if {[pdblsAvailable SpdbMat SSol Poisson]} { 

if {[pdbGetBoolean SpdbMat SSol Poisson]} {set Poiss 1} 



set ni "([pdbGetString SpdbMat SSol niz])" 

if {ISPoiss} { 

set neq "(0.5*(Charge+sqrt(Charge*Charge+4*$ni*$ni))/$ni)" 

term name = Noni add eqn = "exp( Potential * SVti)" SMat 
term name = Poni add eqn = "exp( - Potential * SVti)" SMat 

set eq "Potential * SVti - log(Sneq)" 
pdbSetString SpdbMat SSol Equation Seq 
} else { 

#set a solution variable 

set sols [solution list] 

if {[lsearch Ssols Potential] == -1 } { 

solution add name = Potential solve damp negative 
} 

term name = Noni add eqn = "exp( Potential * SVti)" SMat 
term name = Poni add eqn = "exp( - Potential * SVti)" SMat 

set eps "([pdbGetString SpdbMat SSol Permittivityz] * 8.854e-14 / 1.619e-19)" 
set eq "Seps * grad(Potential) + Sni * (Poni - Noni) + Charge" 
pdbSetString SpdbMat SSol Equation Seq 

} 
} 

proc Potentiallnit { Mat Sol } { 

term name = Charge add eqn = 0.0 SMat 
} 



APPENDIX B 
MODELING THE MOBILITY WITH FLOOPS 

The following file, mobility ex. tcl, can be used with FLOOPS to model the mobility in 
boron implanted silicon. The user must read in the boron profile and supply the 
SIMSdose and hole density (holes). 

struct inf=boron lei 5. struct 
set SIMSdose 5.78el4 
set holes 9. 5e 13 

#L is the width of the circumference... 
setL16.0e-8 
setlntDose 9.27el4 
set LoopDose 8.2e9 

set peract [expr $holes/$SIMSdose] 

sel z=Boron 

set Bdose [FindDose] 

sel z=(($SIMSdose/$Bdose)*Boron) name=Boron store 



sel z=Boron name=NA 

sel z=(NA*$peract) name=NAneg 

sel z=(NA-NAneg) name=NN 

sel z=Boron name=Int 

#atoms/cm2 in plane 
setna 1.5el5 

set NeutralDose [expr $LoopDose*2.0*3. 14 1 59*$L*$na*sqrt($IntDose/($LoopDose*$na*3. 141 59))] 

selz=NN 

set NDose [FindDose] 

sel z=(NN*$NeutralDose/$NDose) name=NNL store 

#set temperature 

set T 300.0 

#/cm3 

set pi 3.14 

set h 6.625e-34 

set hbar [expr "$h / (2.0 * $pi)"] 

setkJ 1.38e-23 

setk 1.38e-23 



153 






154 



setkeV 8.617383e-05 
setmO 9.1e-31 

setepsilonO 8.854e-12 



set epsilons [expr "11.7* SepsilonO"] 

#g/cm3 

set rhos 2.329 

setq 1.602e-19 

#theta is a function of Temperature see ref[l] 
settheta 735.0 

#delta for p-type Si in eV 
set delta [expr $q*0. 044] 

#set energy of holes 

set E n [expr0.036/($keV*$T)]" 

#Model from Sheng S Li Solid State Electronics Vol 21 pi 109-1 117 1978 
setmstarDl [expr0.5685*$m0] 

set mstarD2 [expr 0.41 1 8*$m0] 

set mstarD3 [expr 0.0790*$m0] 

setmstarD [expr 0. 7997* $m0] 

#frompllll(m/s) 

set us 9.037e3 

#D0 (eV/cm) 

set DO [expr5.7e8*100*$q] 

#E1 (eV) 

set El [expr $q*7. 022] 

#effective mass in kg 
setmO 9.1095e-31 
setmstarCl [expr0.4484*$m0] 

setmstarC2 [expr 0.523 l*$m0] 
setmstarC3 [expr0.2517*$m0] 

setmstarC [expr 0.461 6*$m0] 

#reciprocal relaxation time constant for acoustical phonon scattering 

set taual "[expr ([expr 1.414 * pow([expr $q*$El],2.0)*pow($mstarDl ) 1.5)*$k * $T ]* 

(pow(([expr $q*$E]),0.5))) /[expr ($pi * pow($hbar,4.0) * $rhos * pow($us,2.0))]]" 

set taua2 "[expr ([expr 1.414 * pow([expr $q*$El],2.0)*pow($mstarD2,1.5)*$k * $T]* 

(pow(([expr $q*$E]),0.5))) /[expr ($pi * pow($hbar,4.0) * Srhos * pow($us,2.0))]]" 

set taua3 "[expr([expr 1.414 * pow([expr $q*$El],2.0)*pow($mstarD3,1.5)*$k * $T ]* 

(pow(([expr $q*$E]),0.5))) /[expr($pi * pow($hbar,4.0) * Srhos * pow($us,2.0))]]" 

# set taua2 "(1.414 * ($El) A 2.0*$mstarD2 * $k * $T * (SE^.S) / ($pi * ($hbar) A 4.0 * Srhos 
($us) A 2.0)" 



155 



# set taua3 "(1.414 * ($El) A 2.0*$mstarD3 * $k * $T * ($E)*O.S) / ($pi * ($hbar) A 4.0 * Srhos * 
($us) A 2.0)" 



#reciprocal relaxation time constant for optical phonon scattering 
set nO M [exprl.O/(exp($theta/$T))]" 

set x "[expr $E/($keV*$T)]" 

set tauol n [exprpow([expr(2.0*$mstarDl)],1.5)*pow($D0,2.0)*(($n0 + 1 )*pow(([expr $E- 

$keV*$theta]),0.5)+$nO*[exprpow([expr 

$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar,2.0)*$rhos*$k*$theta)]" 

set tauo2 "[exprpow([expr(2.0*$mstarD2)],1.5)*pow($D0,2.0)*(($n0 + 1 )*pow(([expr $E- 

$keV*$theta]),0.5)+$nO*[expr pow([expr 

$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar > 2.0)*$rhos*$k*$theta)]" 

set tauo3 "[exprpow([expr(2.0*$mstarD3)],1.5)*pow($DO,2.0)*(($nO+ l)*pow(([expr $E- 

$keV*$theta]),0.5)+$nO*[exprpow([expr 

$E+$k*$theta],0.5)])/(4.0*$pi*pow($hbar,2.0)*$rhos*$k*$theta)]" 

#lattice mobility 

set tauLl "[expr 1.0/(1.0/($taual)+1.0/($tauol))]" 

set tauL2 "[expr 1.0/(1. 0/($taua2)+1.0/($tauo2))]" 

set tauL3 "[expr 1.0/(1.0/($taua3)+1.0/($tauo3))]" 

set x "[expr ($E/($keV*$T))]" 

setavetauLl "[expr(4.0/(3.0*pow($pi ) 0.5)))*$tauLl*pow($x,1.5)*exp(-$x)*$x]" 
set avetauL2 "[expr (4.0/(3.0*pow($pi,0.5)))*$tauL2*pow($x,l ,5)*exp(-$x)*$x]" 
set avetauL3 "[expr (4.0/(3.0*pow($pi,0.5)))*$tauL3*pow($x,l ,5)*exp(-$x)*$x]" 

set muLl "[expr($q*$avetauLl)/$mstarCl]" 

set muL2 "[expr $q/$mstarC2*$avetauL2]" 

set muL3 "[expr $q/$mstarC3*$avetauL3]" 

set muL "[expr ($muLl+$muL2*[expr pow(($mstarD2 / $mstarDl),1.5)] + $muL3 * [expr pow 

(($mstarD3 / $mstarDl),1.5)]) / [expr (1.0 + pow(($mstarD2 / $mstarDl),1.5) + pow(($mstarD3 / 
$mstarDl),1.5))]]" 

#ionized impurity scattering mobility (Brooks-Herring formula) 

sel z=NAneg name=p 

sel z=(p+NAneg*(l-NAneg/NA)) name=pprime 

sel z=(pprime* 1 0e6) 

sel z=((24.0*$pi*$mstarDl *$epsilons*(($k*$T) A 2.0))/(($q A 2.0)*($h A 2)*pprime)) name=bl 
selz=((24.0*$pi*$mstarD2*$epsilons*(($k*$T) A 2.0))/(($q A 2.0)*($h A 2)*pprime))name=b2 
selz=((24.0*$pi*$mstarD3*$epsilons*(($k*$T) A 2.0))/(($q A 2.0)*($h A 2)*pprime))name=b3 

sel z=(log(bl+1.0)-bl/(bl+1.0)) name=Gatbl 
sel z=(log(b2+1.0)-b2/(b2+1.0)) name=Gatb2 
sel z=(log(b3+1.0)-b3/(b3+1.0)) name=Gatb3 

sel z=NAneg name=NI 



156 



#convert to meters... 

selz=(NI*1.0e6) 

set md 0.01 

set md 1.0 

selz=(((2.0 A 3.5)*($epsilons A 2.0)*($mstarDl A 0.5)*(($k*$T) A 1.5)*$md)/(($pi A 1.5)* 

($q A 3.0)*$mstarCl*NI*Gatbl)) name=mull 

selz=(((2.0 A 3.5)*($epsilons A 2.0)*($mstarD2 A 0.5)*(($k*$T) A 1.5)*$md)/(($pi A 1.5)* 

($q A 3.0)*$mstarC2*NI*Gatb2)) name=muI2 

selz=(((2.0 A 3.5)*($epsilons A 2.0)*($mstarD3 A 0.5)*(($k*$T) A 1.5)* 

$md)/(($pi A 1.5)*($q A 3.0)*$mstarC3*NI*Gatb3))name=muI3 

sel z=((mull +muI2*(($mstarD2/$mstarD 1 ) A 1 . 5)+muI3 *(($mstarD3/$mstarD 1 ) A 1 . 5))/ 

(1.0+(($mstarD2/$mstarDl) A 1.5)+(($mstarD3/$mstarDl) A 1.5)))name=muI 

#neutral impurity scattering 
set md 0.01 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarDl A 2.0*$md))/(5.0*$epsilons*($h A 3.0)* 
SmstarC 1 *NN* 1 . 0e6)) name=muE 1 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarD2 A 2.0*$md))/(5.0*$epsilons*($h A 3.0)* 
$mstarC2*NN*1.0e6)) name=muE2 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarD3 A 2.0*$md))/(5.0*$epsilons*($h A 3.0)* 
$mstarC3*NN* 1 0e6)) name=muE3 

set EN "[expr 1.136e-19 * (SmstarD / $m0) * pow(($epsilon0 / $epsilons),2.0)]" 

selz=(muEl*(0.82*((2.0/3.0)*(($k*$T/$EN) A 0.5)+(1.0/3.0)*($EN/($k*$T) A 0.5))))name=muNl 
selz=(muE2*(0.82*((2.0/3.0)*(($k*$T/$EN) A O.5)+(1.0/3.0)*($EN/($k*$T) A 0.5))))name=muN2 
selz=(muE3*(0.82*((2.0/3.0)*(($k*$T/$EN) A 0.5)+(1.0/3.0)*($EN/($k*$T) A 0.5))))name=muN3 

sel z=((muNl+muN2*(($mstarD2/$mstarD 1 ) A 1 . 5)+muN3 *(($mstarD3/$mstarD 1 ) A 1 . 5))/ 
(1.0+<($mstarD2/$mstarDl) A 1.5)+(($mstarD3/$mstarDl) A 1.5)))name=muN 

#neutral loops impurity scattering 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarDl A 2.0*$md))/(5.0*$epsilons*($h A 3.0)* 
SmstarC 1 *NNL* 1 0e6)) name=muElL 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarD2 A 2.0*$md)V(5.0*$epsilons*($h A 3.0)* 
$mstarC2*NNL*1.0e6)) name=muE2L 

selz=((2.0*($pi A 3.0)*($q A 3.0)*($mstarD3 A 2.0*$md))/(5.0*$epsilons*($h A 3.0)* 
$mstarC3*NNL*1.0e6)) name=muE3L 

set ENL "[expr 1.136e-19 * (SmstarD / $m0) * pow(($epsilon0 / $epsilons),2.0)]" 

selz=(mi£lL*(0.82*((2.0/3.0)*(($k*$T/$ENL) A O.5H10/3.0)*($ENI7($k*$T) A O.5))))name==muNlL 
sel z=(muE2L*(0.82*((2.0/3.0)*(($k*$T/$ENL) A 0.5)+(l ■0/3.0)*($ENL/($k*$T) A 0.5)))) name=muN2L 
selz=(muE3L*(0.82*((2.0/3.0)*(($k*$T/$ENL) A O.5>H10/3.0)*($ENL/($k*$T) A O.5))))name=muN3L 

sel z=((muNl L+muN2L*(($mstarD2/$mstarDl ) A 1 . 5)+muN3L*(($mstarD3/$mstarD 1 ) A 1 . 5))/ 
(1.0-K($mstarD2/$mstarDl) A 1.5)-K($mstarD3/$mstarDl) A 1.5)))name=muNL 

sel z=(1.0/(1.0/$muL+1.0/muI)) name=muLI 

sel z=(1.0/(1.0/muI+1.0/muN+1.0/muNL)) name=muP 

#calculate average mobility 
sel z=muP 
set lm [layers] 
foreach line $lm { 
set avemu [lindex $line 2] 



157 



I 



set mob [expr Savemu] 

puts "The average mobility is $mob cm2/v-s." 

sel z=NAneg 

set naneg [FindDose] 

#puts "Active dose is Snaneg holes/cm2." 

puts "The sheet number is Snaneg holes/cm2." 

set r [expr 1.0/($q*$avemu*$naneg)] 

sel z=1.0/($q*$avemu*$naneg) name=resi stance 

puts "The sheet resistance is $r Ohms/sq." 






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BIOGRAPHICAL SKETCH 
Susan Earles was boron on March 7, 1972, in Rockford, Illinois. She received her 
Bachelor of Science degree in May of 1995 and Master of Science degree in May of 1998 
from the University of Florida. Since then she has worked toward the Ph.D at the 
University of Florida. Her research has focused on the effects of nonmelt laser annealing 
on silicon heavily-doped with boron. 









162 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




Mark E. Law, Chairman 
Professor of Electrical and Computer 
Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




Gijs Bosr 
Professor of Electrical and Computer 
Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




*L 



Sheng S. Li 
Professor of Electrical and Computer 
Engineering 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




Paul Holloway 
Professor of Materials Scfence and 
Engineering 



This dissertation was submitted to the Graduate Faculty of the College of 
Engineering and to the Graduate School and was accepted as partial fulfillment of the 
requirements for the degree of Doctor of Philosophy. 

May 2002 




Pramod Khargonekar 

Dean, College of Engineering 



Winfred Phillips 
Dean, Graduate School 




,£105 



UNIVERSITY OF FLORIDA 

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